xref: /petsc/src/mat/impls/is/matis.c (revision 053abcdfeaa3c4bf7b7c01a7334c7edc5567db03)

/*
    Creates a matrix class for using the Neumann-Neumann type preconditioners.
    This stores the matrices in globally unassembled form. Each processor
    assembles only its local Neumann problem and the parallel matrix vector
    product is handled "implicitly".

    Currently this allows for only one subdomain per processor.
*/

#include <petsc/private/matisimpl.h> /*I "petscmat.h" I*/
#include <../src/mat/impls/aij/mpi/mpiaij.h>
#include <petsc/private/sfimpl.h>
#include <petsc/private/vecimpl.h>
#include <petsc/private/hashseti.h>

#define MATIS_MAX_ENTRIES_INSERTION 2048

/* copied from src/mat/impls/localref/mlocalref.c */
#define IndexSpaceGet(buf, nrow, ncol, irowm, icolm) \
  do { \
    if (nrow + ncol > (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) { \
      PetscCall(PetscMalloc2(nrow, &irowm, ncol, &icolm)); \
    } else { \
      irowm = &buf[0]; \
      icolm = &buf[nrow]; \
    } \
  } while (0)

#define IndexSpaceRestore(buf, nrow, ncol, irowm, icolm) \
  do { \
    if (nrow + ncol > (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) PetscCall(PetscFree2(irowm, icolm)); \
  } while (0)

static void BlockIndicesExpand(PetscInt n, const PetscInt idx[], PetscInt bs, PetscInt idxm[])
{
  for (PetscInt i = 0; i < n; i++) {
    for (PetscInt j = 0; j < bs; j++) idxm[i * bs + j] = idx[i] * bs + j;
  }
}

static PetscErrorCode MatSetValuesLocal_IS(Mat, PetscInt, const PetscInt *, PetscInt, const PetscInt *, const PetscScalar *, InsertMode);
static PetscErrorCode MatSetValuesBlockedLocal_IS(Mat, PetscInt, const PetscInt *, PetscInt, const PetscInt *, const PetscScalar *, InsertMode);
static PetscErrorCode MatISSetUpScatters_Private(Mat);

static PetscErrorCode MatISContainerDestroyPtAP_Private(void **ptr)
{
  MatISPtAP ptap = (MatISPtAP)*ptr;

  PetscFunctionBegin;
  PetscCall(MatDestroySubMatrices(ptap->ris1 ? 2 : 1, &ptap->lP));
  PetscCall(ISDestroy(&ptap->cis0));
  PetscCall(ISDestroy(&ptap->cis1));
  PetscCall(ISDestroy(&ptap->ris0));
  PetscCall(ISDestroy(&ptap->ris1));
  PetscCall(PetscFree(ptap));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatPtAPNumeric_IS_XAIJ(Mat A, Mat P, Mat C)
{
  MatISPtAP      ptap;
  Mat_IS        *matis = (Mat_IS *)A->data;
  Mat            lA, lC;
  MatReuse       reuse;
  IS             ris[2], cis[2];
  PetscContainer c;
  PetscInt       n;

  PetscFunctionBegin;
  PetscCall(PetscObjectQuery((PetscObject)C, "_MatIS_PtAP", (PetscObject *)&c));
  PetscCheck(c, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing PtAP information");
  PetscCall(PetscContainerGetPointer(c, (void **)&ptap));
  ris[0] = ptap->ris0;
  ris[1] = ptap->ris1;
  cis[0] = ptap->cis0;
  cis[1] = ptap->cis1;
  n      = ptap->ris1 ? 2 : 1;
  reuse  = ptap->lP ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;
  PetscCall(MatCreateSubMatrices(P, n, ris, cis, reuse, &ptap->lP));

  PetscCall(MatISGetLocalMat(A, &lA));
  PetscCall(MatISGetLocalMat(C, &lC));
  if (ptap->ris1) { /* unsymmetric A mapping */
    Mat lPt;

    PetscCall(MatTranspose(ptap->lP[1], MAT_INITIAL_MATRIX, &lPt));
    PetscCall(MatMatMatMult(lPt, lA, ptap->lP[0], reuse, ptap->fill, &lC));
    if (matis->storel2l) PetscCall(PetscObjectCompose((PetscObject)A, "_MatIS_PtAP_l2l", (PetscObject)lPt));
    PetscCall(MatDestroy(&lPt));
  } else {
    PetscCall(MatPtAP(lA, ptap->lP[0], reuse, ptap->fill, &lC));
    if (matis->storel2l) PetscCall(PetscObjectCompose((PetscObject)C, "_MatIS_PtAP_l2l", (PetscObject)ptap->lP[0]));
  }
  if (reuse == MAT_INITIAL_MATRIX) {
    PetscCall(MatISSetLocalMat(C, lC));
    PetscCall(MatDestroy(&lC));
  }
  PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetNonzeroColumnsLocal_Private(Mat PT, IS *cis)
{
  Mat             Po, Pd;
  IS              zd, zo;
  const PetscInt *garray;
  PetscInt       *aux, i, bs;
  PetscInt        dc, stc, oc, ctd, cto;
  PetscBool       ismpiaij, ismpibaij, isseqaij, isseqbaij;
  MPI_Comm        comm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(PT, MAT_CLASSID, 1);
  PetscAssertPointer(cis, 2);
  PetscCall(PetscObjectGetComm((PetscObject)PT, &comm));
  bs = 1;
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)PT, MATMPIAIJ, &ismpiaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)PT, MATMPIBAIJ, &ismpibaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)PT, MATSEQAIJ, &isseqaij));
  PetscCall(PetscObjectTypeCompare((PetscObject)PT, MATSEQBAIJ, &isseqbaij));
  if (isseqaij || isseqbaij) {
    Pd     = PT;
    Po     = NULL;
    garray = NULL;
  } else if (ismpiaij) {
    PetscCall(MatMPIAIJGetSeqAIJ(PT, &Pd, &Po, &garray));
  } else if (ismpibaij) {
    PetscCall(MatMPIBAIJGetSeqBAIJ(PT, &Pd, &Po, &garray));
    PetscCall(MatGetBlockSize(PT, &bs));
  } else SETERRQ(comm, PETSC_ERR_SUP, "Not for matrix type %s", ((PetscObject)PT)->type_name);

  /* identify any null columns in Pd or Po */
  /* We use a tolerance comparison since it may happen that, with geometric multigrid,
     some of the columns are not really zero, but very close to */
  zo = zd = NULL;
  if (Po) PetscCall(MatFindNonzeroRowsOrCols_Basic(Po, PETSC_TRUE, PETSC_SMALL, &zo));
  PetscCall(MatFindNonzeroRowsOrCols_Basic(Pd, PETSC_TRUE, PETSC_SMALL, &zd));

  PetscCall(MatGetLocalSize(PT, NULL, &dc));
  PetscCall(MatGetOwnershipRangeColumn(PT, &stc, NULL));
  if (Po) PetscCall(MatGetLocalSize(Po, NULL, &oc));
  else oc = 0;
  PetscCall(PetscMalloc1((dc + oc) / bs, &aux));
  if (zd) {
    const PetscInt *idxs;
    PetscInt        nz;

    /* this will throw an error if bs is not valid */
    PetscCall(ISSetBlockSize(zd, bs));
    PetscCall(ISGetLocalSize(zd, &nz));
    PetscCall(ISGetIndices(zd, &idxs));
    ctd = nz / bs;
    for (i = 0; i < ctd; i++) aux[i] = (idxs[bs * i] + stc) / bs;
    PetscCall(ISRestoreIndices(zd, &idxs));
  } else {
    ctd = dc / bs;
    for (i = 0; i < ctd; i++) aux[i] = i + stc / bs;
  }
  if (zo) {
    const PetscInt *idxs;
    PetscInt        nz;

    /* this will throw an error if bs is not valid */
    PetscCall(ISSetBlockSize(zo, bs));
    PetscCall(ISGetLocalSize(zo, &nz));
    PetscCall(ISGetIndices(zo, &idxs));
    cto = nz / bs;
    for (i = 0; i < cto; i++) aux[i + ctd] = garray[idxs[bs * i] / bs];
    PetscCall(ISRestoreIndices(zo, &idxs));
  } else {
    cto = oc / bs;
    for (i = 0; i < cto; i++) aux[i + ctd] = garray[i];
  }
  PetscCall(ISCreateBlock(comm, bs, ctd + cto, aux, PETSC_OWN_POINTER, cis));
  PetscCall(ISDestroy(&zd));
  PetscCall(ISDestroy(&zo));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatPtAPSymbolic_IS_XAIJ(Mat A, Mat P, PetscReal fill, Mat C)
{
  Mat                    PT, lA;
  MatISPtAP              ptap;
  ISLocalToGlobalMapping Crl2g, Ccl2g, rl2g, cl2g;
  PetscContainer         c;
  MatType                lmtype;
  const PetscInt        *garray;
  PetscInt               ibs, N, dc;
  MPI_Comm               comm;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCall(MatSetType(C, MATIS));
  PetscCall(MatISGetLocalMat(A, &lA));
  PetscCall(MatGetType(lA, &lmtype));
  PetscCall(MatISSetLocalMatType(C, lmtype));
  PetscCall(MatGetSize(P, NULL, &N));
  PetscCall(MatGetLocalSize(P, NULL, &dc));
  PetscCall(MatSetSizes(C, dc, dc, N, N));
  /* Not sure about this
  PetscCall(MatGetBlockSizes(P,NULL,&ibs));
  PetscCall(MatSetBlockSize(*C,ibs));
*/

  PetscCall(PetscNew(&ptap));
  PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &c));
  PetscCall(PetscContainerSetPointer(c, ptap));
  PetscCall(PetscContainerSetCtxDestroy(c, MatISContainerDestroyPtAP_Private));
  PetscCall(PetscObjectCompose((PetscObject)C, "_MatIS_PtAP", (PetscObject)c));
  PetscCall(PetscContainerDestroy(&c));
  ptap->fill = fill;

  PetscCall(MatISGetLocalToGlobalMapping(A, &rl2g, &cl2g));

  PetscCall(ISLocalToGlobalMappingGetBlockSize(cl2g, &ibs));
  PetscCall(ISLocalToGlobalMappingGetSize(cl2g, &N));
  PetscCall(ISLocalToGlobalMappingGetBlockIndices(cl2g, &garray));
  PetscCall(ISCreateBlock(comm, ibs, N / ibs, garray, PETSC_COPY_VALUES, &ptap->ris0));
  PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(cl2g, &garray));

  PetscCall(MatCreateSubMatrix(P, ptap->ris0, NULL, MAT_INITIAL_MATRIX, &PT));
  PetscCall(MatGetNonzeroColumnsLocal_Private(PT, &ptap->cis0));
  PetscCall(ISLocalToGlobalMappingCreateIS(ptap->cis0, &Ccl2g));
  PetscCall(MatDestroy(&PT));

  Crl2g = NULL;
  if (rl2g != cl2g) { /* unsymmetric A mapping */
    PetscBool same, lsame = PETSC_FALSE;
    PetscInt  N1, ibs1;

    PetscCall(ISLocalToGlobalMappingGetSize(rl2g, &N1));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(rl2g, &ibs1));
    PetscCall(ISLocalToGlobalMappingGetBlockIndices(rl2g, &garray));
    PetscCall(ISCreateBlock(comm, ibs, N1 / ibs, garray, PETSC_COPY_VALUES, &ptap->ris1));
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(rl2g, &garray));
    if (ibs1 == ibs && N1 == N) { /* check if the l2gmaps are the same */
      const PetscInt *i1, *i2;

      PetscCall(ISBlockGetIndices(ptap->ris0, &i1));
      PetscCall(ISBlockGetIndices(ptap->ris1, &i2));
      PetscCall(PetscArraycmp(i1, i2, N, &lsame));
    }
    PetscCallMPI(MPIU_Allreduce(&lsame, &same, 1, MPI_C_BOOL, MPI_LAND, comm));
    if (same) {
      PetscCall(ISDestroy(&ptap->ris1));
    } else {
      PetscCall(MatCreateSubMatrix(P, ptap->ris1, NULL, MAT_INITIAL_MATRIX, &PT));
      PetscCall(MatGetNonzeroColumnsLocal_Private(PT, &ptap->cis1));
      PetscCall(ISLocalToGlobalMappingCreateIS(ptap->cis1, &Crl2g));
      PetscCall(MatDestroy(&PT));
    }
  }
  /* Not sure about this
  if (!Crl2g) {
    PetscCall(MatGetBlockSize(C,&ibs));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(Ccl2g,ibs));
  }
*/
  PetscCall(MatSetLocalToGlobalMapping(C, Crl2g ? Crl2g : Ccl2g, Ccl2g));
  PetscCall(ISLocalToGlobalMappingDestroy(&Crl2g));
  PetscCall(ISLocalToGlobalMappingDestroy(&Ccl2g));

  C->ops->ptapnumeric = MatPtAPNumeric_IS_XAIJ;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductSymbolic_PtAP_IS_XAIJ(Mat C)
{
  Mat_Product *product = C->product;
  Mat          A = product->A, P = product->B;
  PetscReal    fill = product->fill;

  PetscFunctionBegin;
  PetscCall(MatPtAPSymbolic_IS_XAIJ(A, P, fill, C));
  C->ops->productnumeric = MatProductNumeric_PtAP;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatProductSetFromOptions_IS_XAIJ_PtAP(Mat C)
{
  PetscFunctionBegin;
  C->ops->productsymbolic = MatProductSymbolic_PtAP_IS_XAIJ;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat C)
{
  Mat_Product *product = C->product;

  PetscFunctionBegin;
  if (product->type == MATPRODUCT_PtAP) PetscCall(MatProductSetFromOptions_IS_XAIJ_PtAP(C));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISContainerDestroyFields_Private(void **ptr)
{
  MatISLocalFields lf = (MatISLocalFields)*ptr;
  PetscInt         i;

  PetscFunctionBegin;
  for (i = 0; i < lf->nr; i++) PetscCall(ISDestroy(&lf->rf[i]));
  for (i = 0; i < lf->nc; i++) PetscCall(ISDestroy(&lf->cf[i]));
  PetscCall(PetscFree2(lf->rf, lf->cf));
  PetscCall(PetscFree(lf));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatConvert_SeqXAIJ_IS(Mat A, MatType type, MatReuse reuse, Mat *newmat)
{
  Mat B, lB;

  PetscFunctionBegin;
  if (reuse != MAT_REUSE_MATRIX) {
    ISLocalToGlobalMapping rl2g, cl2g;
    PetscInt               bs;
    IS                     is;

    PetscCall(MatGetBlockSize(A, &bs));
    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), A->rmap->n / bs, 0, 1, &is));
    if (bs > 1) {
      IS       is2;
      PetscInt i, *aux;

      PetscCall(ISGetLocalSize(is, &i));
      PetscCall(ISGetIndices(is, (const PetscInt **)&aux));
      PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)A), bs, i, aux, PETSC_COPY_VALUES, &is2));
      PetscCall(ISRestoreIndices(is, (const PetscInt **)&aux));
      PetscCall(ISDestroy(&is));
      is = is2;
    }
    PetscCall(ISSetIdentity(is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &rl2g));
    PetscCall(ISDestroy(&is));
    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), A->cmap->n / bs, 0, 1, &is));
    if (bs > 1) {
      IS       is2;
      PetscInt i, *aux;

      PetscCall(ISGetLocalSize(is, &i));
      PetscCall(ISGetIndices(is, (const PetscInt **)&aux));
      PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)A), bs, i, aux, PETSC_COPY_VALUES, &is2));
      PetscCall(ISRestoreIndices(is, (const PetscInt **)&aux));
      PetscCall(ISDestroy(&is));
      is = is2;
    }
    PetscCall(ISSetIdentity(is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &cl2g));
    PetscCall(ISDestroy(&is));
    PetscCall(MatCreateIS(PetscObjectComm((PetscObject)A), bs, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, rl2g, cl2g, &B));
    PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
    PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
    PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &lB));
    if (reuse == MAT_INITIAL_MATRIX) *newmat = B;
  } else {
    B = *newmat;
    PetscCall(PetscObjectReference((PetscObject)A));
    lB = A;
  }
  PetscCall(MatISSetLocalMat(B, lB));
  PetscCall(MatDestroy(&lB));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISScaleDisassembling_Private(Mat A)
{
  Mat_IS         *matis = (Mat_IS *)A->data;
  PetscScalar    *aa;
  const PetscInt *ii, *jj;
  PetscInt        i, n, m;
  PetscInt       *ecount, **eneighs;
  PetscBool       flg;

  PetscFunctionBegin;
  PetscCall(MatGetRowIJ(matis->A, 0, PETSC_FALSE, PETSC_FALSE, &m, &ii, &jj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot get IJ structure");
  PetscCall(ISLocalToGlobalMappingGetNodeInfo(matis->rmapping, &n, &ecount, &eneighs));
  PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected %" PetscInt_FMT " != %" PetscInt_FMT, m, n);
  PetscCall(MatSeqAIJGetArray(matis->A, &aa));
  for (i = 0; i < n; i++) {
    if (ecount[i] > 1) {
      PetscInt j;

      for (j = ii[i]; j < ii[i + 1]; j++) {
        PetscInt  i2   = jj[j], p, p2;
        PetscReal scal = 0.0;

        for (p = 0; p < ecount[i]; p++) {
          for (p2 = 0; p2 < ecount[i2]; p2++) {
            if (eneighs[i][p] == eneighs[i2][p2]) {
              scal += 1.0;
              break;
            }
          }
        }
        if (scal) aa[j] /= scal;
      }
    }
  }
  PetscCall(ISLocalToGlobalMappingRestoreNodeInfo(matis->rmapping, &n, &ecount, &eneighs));
  PetscCall(MatSeqAIJRestoreArray(matis->A, &aa));
  PetscCall(MatRestoreRowIJ(matis->A, 0, PETSC_FALSE, PETSC_FALSE, &m, &ii, &jj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot restore IJ structure");
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef enum {
  MAT_IS_DISASSEMBLE_L2G_NATURAL,
  MAT_IS_DISASSEMBLE_L2G_MAT,
  MAT_IS_DISASSEMBLE_L2G_ND
} MatISDisassemblel2gType;

static PetscErrorCode MatMPIXAIJComputeLocalToGlobalMapping_Private(Mat A, ISLocalToGlobalMapping *l2g)
{
  Mat                     Ad, Ao;
  IS                      is, ndmap, ndsub;
  MPI_Comm                comm;
  const PetscInt         *garray, *ndmapi;
  PetscInt                bs, i, cnt, nl, *ncount, *ndmapc;
  PetscBool               ismpiaij, ismpibaij;
  const char *const       MatISDisassemblel2gTypes[] = {"NATURAL", "MAT", "ND", "MatISDisassemblel2gType", "MAT_IS_DISASSEMBLE_L2G_", NULL};
  MatISDisassemblel2gType mode                       = MAT_IS_DISASSEMBLE_L2G_NATURAL;
  MatPartitioning         part;
  PetscSF                 sf;
  PetscObject             dm;

  PetscFunctionBegin;
  PetscOptionsBegin(PetscObjectComm((PetscObject)A), ((PetscObject)A)->prefix, "MatIS l2g disassembling options", "Mat");
  PetscCall(PetscOptionsEnum("-mat_is_disassemble_l2g_type", "Type of local-to-global mapping to be used for disassembling", "MatISDisassemblel2gType", MatISDisassemblel2gTypes, (PetscEnum)mode, (PetscEnum *)&mode, NULL));
  PetscOptionsEnd();
  if (mode == MAT_IS_DISASSEMBLE_L2G_MAT) {
    PetscCall(MatGetLocalToGlobalMapping(A, l2g, NULL));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &ismpiaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIBAIJ, &ismpibaij));
  PetscCall(MatGetBlockSize(A, &bs));
  switch (mode) {
  case MAT_IS_DISASSEMBLE_L2G_ND:
    PetscCall(MatPartitioningCreate(comm, &part));
    PetscCall(MatPartitioningSetAdjacency(part, A));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)part, ((PetscObject)A)->prefix));
    PetscCall(MatPartitioningSetFromOptions(part));
    PetscCall(MatPartitioningApplyND(part, &ndmap));
    PetscCall(MatPartitioningDestroy(&part));
    PetscCall(ISBuildTwoSided(ndmap, NULL, &ndsub));
    PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, PETSC_TRUE));
    PetscCall(MatIncreaseOverlap(A, 1, &ndsub, 1));
    PetscCall(ISLocalToGlobalMappingCreateIS(ndsub, l2g));

    /* it may happen that a separator node is not properly shared */
    PetscCall(ISLocalToGlobalMappingGetNodeInfo(*l2g, &nl, &ncount, NULL));
    PetscCall(PetscSFCreate(comm, &sf));
    PetscCall(ISLocalToGlobalMappingGetIndices(*l2g, &garray));
    PetscCall(PetscSFSetGraphLayout(sf, A->rmap, nl, NULL, PETSC_OWN_POINTER, garray));
    PetscCall(ISLocalToGlobalMappingRestoreIndices(*l2g, &garray));
    PetscCall(PetscCalloc1(A->rmap->n, &ndmapc));
    PetscCall(PetscSFReduceBegin(sf, MPIU_INT, ncount, ndmapc, MPI_REPLACE));
    PetscCall(PetscSFReduceEnd(sf, MPIU_INT, ncount, ndmapc, MPI_REPLACE));
    PetscCall(ISLocalToGlobalMappingRestoreNodeInfo(*l2g, NULL, &ncount, NULL));
    PetscCall(ISGetIndices(ndmap, &ndmapi));
    for (i = 0, cnt = 0; i < A->rmap->n; i++)
      if (ndmapi[i] < 0 && ndmapc[i] < 2) cnt++;

    PetscCallMPI(MPIU_Allreduce(&cnt, &i, 1, MPIU_INT, MPI_MAX, comm));
    if (i) { /* we detected isolated separator nodes */
      Mat                    A2, A3;
      IS                    *workis, is2;
      PetscScalar           *vals;
      PetscInt               gcnt = i, *dnz, *onz, j, *lndmapi;
      ISLocalToGlobalMapping ll2g;
      PetscBool              flg;
      const PetscInt        *ii, *jj;

      /* communicate global id of separators */
      MatPreallocateBegin(comm, A->rmap->n, A->cmap->n, dnz, onz);
      for (i = 0, cnt = 0; i < A->rmap->n; i++) dnz[i] = ndmapi[i] < 0 ? i + A->rmap->rstart : -1;

      PetscCall(PetscMalloc1(nl, &lndmapi));
      PetscCall(PetscSFBcastBegin(sf, MPIU_INT, dnz, lndmapi, MPI_REPLACE));

      /* compute adjacency of isolated separators node */
      PetscCall(PetscMalloc1(gcnt, &workis));
      for (i = 0, cnt = 0; i < A->rmap->n; i++) {
        if (ndmapi[i] < 0 && ndmapc[i] < 2) PetscCall(ISCreateStride(comm, 1, i + A->rmap->rstart, 1, &workis[cnt++]));
      }
      for (i = cnt; i < gcnt; i++) PetscCall(ISCreateStride(comm, 0, 0, 1, &workis[i]));
      for (i = 0; i < gcnt; i++) {
        PetscCall(PetscObjectSetName((PetscObject)workis[i], "ISOLATED"));
        PetscCall(ISViewFromOptions(workis[i], NULL, "-view_isolated_separators"));
      }

      /* no communications since all the ISes correspond to locally owned rows */
      PetscCall(MatIncreaseOverlap(A, gcnt, workis, 1));

      /* end communicate global id of separators */
      PetscCall(PetscSFBcastEnd(sf, MPIU_INT, dnz, lndmapi, MPI_REPLACE));

      /* communicate new layers : create a matrix and transpose it */
      PetscCall(PetscArrayzero(dnz, A->rmap->n));
      PetscCall(PetscArrayzero(onz, A->rmap->n));
      for (i = 0, j = 0; i < A->rmap->n; i++) {
        if (ndmapi[i] < 0 && ndmapc[i] < 2) {
          const PetscInt *idxs;
          PetscInt        s;

          PetscCall(ISGetLocalSize(workis[j], &s));
          PetscCall(ISGetIndices(workis[j], &idxs));
          PetscCall(MatPreallocateSet(i + A->rmap->rstart, s, idxs, dnz, onz));
          j++;
        }
      }
      PetscCheck(j == cnt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected local count %" PetscInt_FMT " != %" PetscInt_FMT, j, cnt);

      for (i = 0; i < gcnt; i++) {
        PetscCall(PetscObjectSetName((PetscObject)workis[i], "EXTENDED"));
        PetscCall(ISViewFromOptions(workis[i], NULL, "-view_isolated_separators"));
      }

      for (i = 0, j = 0; i < A->rmap->n; i++) j = PetscMax(j, dnz[i] + onz[i]);
      PetscCall(PetscMalloc1(j, &vals));
      for (i = 0; i < j; i++) vals[i] = 1.0;

      PetscCall(MatCreate(comm, &A2));
      PetscCall(MatSetType(A2, MATMPIAIJ));
      PetscCall(MatSetSizes(A2, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
      PetscCall(MatMPIAIJSetPreallocation(A2, 0, dnz, 0, onz));
      PetscCall(MatSetOption(A2, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
      for (i = 0, j = 0; i < A2->rmap->n; i++) {
        PetscInt        row = i + A2->rmap->rstart, s = dnz[i] + onz[i];
        const PetscInt *idxs;

        if (s) {
          PetscCall(ISGetIndices(workis[j], &idxs));
          PetscCall(MatSetValues(A2, 1, &row, s, idxs, vals, INSERT_VALUES));
          PetscCall(ISRestoreIndices(workis[j], &idxs));
          j++;
        }
      }
      PetscCheck(j == cnt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected local count %" PetscInt_FMT " != %" PetscInt_FMT, j, cnt);
      PetscCall(PetscFree(vals));
      PetscCall(MatAssemblyBegin(A2, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(A2, MAT_FINAL_ASSEMBLY));
      PetscCall(MatTranspose(A2, MAT_INPLACE_MATRIX, &A2));

      /* extract submatrix corresponding to the coupling "owned separators" x "isolated separators" */
      for (i = 0, j = 0; i < nl; i++)
        if (lndmapi[i] >= 0) lndmapi[j++] = lndmapi[i];
      PetscCall(ISCreateGeneral(comm, j, lndmapi, PETSC_USE_POINTER, &is));
      PetscCall(MatMPIAIJGetLocalMatCondensed(A2, MAT_INITIAL_MATRIX, &is, NULL, &A3));
      PetscCall(ISDestroy(&is));
      PetscCall(MatDestroy(&A2));

      /* extend local to global map to include connected isolated separators */
      PetscCall(PetscObjectQuery((PetscObject)A3, "_petsc_GetLocalMatCondensed_iscol", (PetscObject *)&is));
      PetscCheck(is, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing column map");
      PetscCall(ISLocalToGlobalMappingCreateIS(is, &ll2g));
      PetscCall(MatGetRowIJ(A3, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &flg));
      PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot get IJ structure");
      PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ii[i], jj, PETSC_COPY_VALUES, &is));
      PetscCall(MatRestoreRowIJ(A3, 0, PETSC_FALSE, PETSC_FALSE, &i, &ii, &jj, &flg));
      PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot get IJ structure");
      PetscCall(ISLocalToGlobalMappingApplyIS(ll2g, is, &is2));
      PetscCall(ISDestroy(&is));
      PetscCall(ISLocalToGlobalMappingDestroy(&ll2g));

      /* add new nodes to the local-to-global map */
      PetscCall(ISLocalToGlobalMappingDestroy(l2g));
      PetscCall(ISExpand(ndsub, is2, &is));
      PetscCall(ISDestroy(&is2));
      PetscCall(ISLocalToGlobalMappingCreateIS(is, l2g));
      PetscCall(ISDestroy(&is));

      PetscCall(MatDestroy(&A3));
      PetscCall(PetscFree(lndmapi));
      MatPreallocateEnd(dnz, onz);
      for (i = 0; i < gcnt; i++) PetscCall(ISDestroy(&workis[i]));
      PetscCall(PetscFree(workis));
    }
    PetscCall(ISRestoreIndices(ndmap, &ndmapi));
    PetscCall(PetscSFDestroy(&sf));
    PetscCall(PetscFree(ndmapc));
    PetscCall(ISDestroy(&ndmap));
    PetscCall(ISDestroy(&ndsub));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(*l2g, bs));
    PetscCall(ISLocalToGlobalMappingViewFromOptions(*l2g, NULL, "-mat_is_nd_l2g_view"));
    break;
  case MAT_IS_DISASSEMBLE_L2G_NATURAL:
    PetscCall(PetscObjectQuery((PetscObject)A, "__PETSc_dm", &dm));
    if (dm) { /* if a matrix comes from a DM, most likely we can use the l2gmap if any */
      PetscCall(MatGetLocalToGlobalMapping(A, l2g, NULL));
      PetscCall(PetscObjectReference((PetscObject)*l2g));
      if (*l2g) PetscFunctionReturn(PETSC_SUCCESS);
    }
    if (ismpiaij) {
      PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &garray));
    } else if (ismpibaij) {
      PetscCall(MatMPIBAIJGetSeqBAIJ(A, &Ad, &Ao, &garray));
    } else SETERRQ(comm, PETSC_ERR_SUP, "Type %s", ((PetscObject)A)->type_name);
    if (A->rmap->n) {
      PetscInt dc, oc, stc, *aux;

      PetscCall(MatGetLocalSize(Ad, NULL, &dc));
      PetscCall(MatGetLocalSize(Ao, NULL, &oc));
      PetscCheck(!oc || garray, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "garray not present");
      PetscCall(MatGetOwnershipRangeColumn(A, &stc, NULL));
      PetscCall(PetscMalloc1((dc + oc) / bs, &aux));
      for (i = 0; i < dc / bs; i++) aux[i] = i + stc / bs;
      for (i = 0; i < oc / bs; i++) aux[i + dc / bs] = (ismpiaij ? garray[i * bs] / bs : garray[i]);
      PetscCall(ISCreateBlock(comm, bs, (dc + oc) / bs, aux, PETSC_OWN_POINTER, &is));
    } else {
      PetscCall(ISCreateBlock(comm, 1, 0, NULL, PETSC_OWN_POINTER, &is));
    }
    PetscCall(ISLocalToGlobalMappingCreateIS(is, l2g));
    PetscCall(ISDestroy(&is));
    break;
  default:
    SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Unsupported l2g disassembling type %d", mode);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat A, MatType type, MatReuse reuse, Mat *newmat)
{
  Mat                    lA, Ad, Ao, B = NULL;
  ISLocalToGlobalMapping rl2g, cl2g;
  IS                     is;
  MPI_Comm               comm;
  void                  *ptrs[2];
  const char            *names[2] = {"_convert_csr_aux", "_convert_csr_data"};
  const PetscInt        *garray;
  PetscScalar           *dd, *od, *aa, *data;
  const PetscInt        *di, *dj, *oi, *oj;
  const PetscInt        *odi, *odj, *ooi, *ooj;
  PetscInt              *aux, *ii, *jj;
  PetscInt               rbs, cbs, lc, dr, dc, oc, str, stc, nnz, i, jd, jo, cum;
  PetscBool              flg, ismpiaij, ismpibaij, was_inplace = PETSC_FALSE, cong;
  PetscMPIInt            size;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  if (size == 1) {
    PetscCall(MatConvert_SeqXAIJ_IS(A, type, reuse, newmat));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
  PetscCall(MatHasCongruentLayouts(A, &cong));
  if (reuse != MAT_REUSE_MATRIX && cong && rbs == cbs) {
    PetscCall(MatMPIXAIJComputeLocalToGlobalMapping_Private(A, &rl2g));
    PetscCall(MatCreate(comm, &B));
    PetscCall(MatSetType(B, MATIS));
    PetscCall(MatSetSizes(B, A->rmap->n, A->rmap->n, A->rmap->N, A->rmap->N));
    PetscCall(MatSetLocalToGlobalMapping(B, rl2g, rl2g));
    PetscCall(MatSetBlockSizes(B, rbs, rbs));
    PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
    if (reuse == MAT_INPLACE_MATRIX) was_inplace = PETSC_TRUE;
    reuse = MAT_REUSE_MATRIX;
  }
  if (reuse == MAT_REUSE_MATRIX) {
    Mat            *newlA, lA;
    IS              rows, cols;
    const PetscInt *ridx, *cidx;
    PetscInt        nr, nc;

    if (!B) B = *newmat;
    PetscCall(MatISGetLocalToGlobalMapping(B, &rl2g, &cl2g));
    PetscCall(ISLocalToGlobalMappingGetBlockIndices(rl2g, &ridx));
    PetscCall(ISLocalToGlobalMappingGetBlockIndices(cl2g, &cidx));
    PetscCall(ISLocalToGlobalMappingGetSize(rl2g, &nr));
    PetscCall(ISLocalToGlobalMappingGetSize(cl2g, &nc));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(rl2g, &rbs));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(cl2g, &cbs));
    PetscCall(ISCreateBlock(comm, rbs, nr / rbs, ridx, PETSC_USE_POINTER, &rows));
    if (rl2g != cl2g) {
      PetscCall(ISCreateBlock(comm, cbs, nc / cbs, cidx, PETSC_USE_POINTER, &cols));
    } else {
      PetscCall(PetscObjectReference((PetscObject)rows));
      cols = rows;
    }
    PetscCall(MatISGetLocalMat(B, &lA));
    PetscCall(MatCreateSubMatrices(A, 1, &rows, &cols, MAT_INITIAL_MATRIX, &newlA));
    PetscCall(MatConvert(newlA[0], MATSEQAIJ, MAT_INPLACE_MATRIX, &newlA[0]));
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(rl2g, &ridx));
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(cl2g, &cidx));
    PetscCall(ISDestroy(&rows));
    PetscCall(ISDestroy(&cols));
    if (!lA->preallocated) { /* first time */
      PetscCall(MatDuplicate(newlA[0], MAT_COPY_VALUES, &lA));
      PetscCall(MatISSetLocalMat(B, lA));
      PetscCall(PetscObjectDereference((PetscObject)lA));
    }
    PetscCall(MatCopy(newlA[0], lA, SAME_NONZERO_PATTERN));
    PetscCall(MatDestroySubMatrices(1, &newlA));
    PetscCall(MatISScaleDisassembling_Private(B));
    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    if (was_inplace) PetscCall(MatHeaderReplace(A, &B));
    else *newmat = B;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* general case, just compress out the column space */
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &ismpiaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIBAIJ, &ismpibaij));
  if (ismpiaij) {
    cbs = 1; /* We cannot guarantee the off-process matrix will respect the column block size */
    PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &garray));
  } else if (ismpibaij) {
    PetscCall(MatMPIBAIJGetSeqBAIJ(A, &Ad, &Ao, &garray));
    PetscCall(MatConvert(Ad, MATSEQAIJ, MAT_INITIAL_MATRIX, &Ad));
    PetscCall(MatConvert(Ao, MATSEQAIJ, MAT_INITIAL_MATRIX, &Ao));
  } else SETERRQ(comm, PETSC_ERR_SUP, "Type %s", ((PetscObject)A)->type_name);
  PetscCall(MatSeqAIJGetArray(Ad, &dd));
  PetscCall(MatSeqAIJGetArray(Ao, &od));

  /* access relevant information from MPIAIJ */
  PetscCall(MatGetOwnershipRange(A, &str, NULL));
  PetscCall(MatGetOwnershipRangeColumn(A, &stc, NULL));
  PetscCall(MatGetLocalSize(Ad, &dr, &dc));
  PetscCall(MatGetLocalSize(Ao, NULL, &oc));
  PetscCheck(!oc || garray, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "garray not present");

  PetscCall(MatGetRowIJ(Ad, 0, PETSC_FALSE, PETSC_FALSE, &i, &di, &dj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot get IJ structure");
  PetscCall(MatGetRowIJ(Ao, 0, PETSC_FALSE, PETSC_FALSE, &i, &oi, &oj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot get IJ structure");
  nnz = di[dr] + oi[dr];
  /* store original pointers to be restored later */
  odi = di;
  odj = dj;
  ooi = oi;
  ooj = oj;

  /* generate l2g maps for rows and cols */
  PetscCall(ISCreateStride(comm, dr / rbs, str / rbs, 1, &is));
  if (rbs > 1) {
    IS is2;

    PetscCall(ISGetLocalSize(is, &i));
    PetscCall(ISGetIndices(is, (const PetscInt **)&aux));
    PetscCall(ISCreateBlock(comm, rbs, i, aux, PETSC_COPY_VALUES, &is2));
    PetscCall(ISRestoreIndices(is, (const PetscInt **)&aux));
    PetscCall(ISDestroy(&is));
    is = is2;
  }
  PetscCall(ISLocalToGlobalMappingCreateIS(is, &rl2g));
  PetscCall(ISDestroy(&is));
  if (dr) {
    PetscCall(PetscMalloc1((dc + oc) / cbs, &aux));
    for (i = 0; i < dc / cbs; i++) aux[i] = i + stc / cbs;
    for (i = 0; i < oc / cbs; i++) aux[i + dc / cbs] = garray[i];
    PetscCall(ISCreateBlock(comm, cbs, (dc + oc) / cbs, aux, PETSC_OWN_POINTER, &is));
    lc = dc + oc;
  } else {
    PetscCall(ISCreateBlock(comm, cbs, 0, NULL, PETSC_OWN_POINTER, &is));
    lc = 0;
  }
  PetscCall(ISLocalToGlobalMappingCreateIS(is, &cl2g));
  PetscCall(ISDestroy(&is));

  /* create MATIS object */
  PetscCall(MatCreate(comm, &B));
  PetscCall(MatSetSizes(B, dr, dc, PETSC_DECIDE, PETSC_DECIDE));
  PetscCall(MatSetType(B, MATIS));
  PetscCall(MatSetBlockSizes(B, rbs, cbs));
  PetscCall(MatSetLocalToGlobalMapping(B, rl2g, cl2g));
  PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
  PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));

  /* merge local matrices */
  PetscCall(PetscMalloc1(nnz + dr + 1, &aux));
  PetscCall(PetscMalloc1(nnz, &data));
  ii  = aux;
  jj  = aux + dr + 1;
  aa  = data;
  *ii = *(di++) + *(oi++);
  for (jd = 0, jo = 0, cum = 0; *ii < nnz; cum++) {
    for (; jd < *di; jd++) {
      *jj++ = *dj++;
      *aa++ = *dd++;
    }
    for (; jo < *oi; jo++) {
      *jj++ = *oj++ + dc;
      *aa++ = *od++;
    }
    *(++ii) = *(di++) + *(oi++);
  }
  for (; cum < dr; cum++) *(++ii) = nnz;

  PetscCall(MatRestoreRowIJ(Ad, 0, PETSC_FALSE, PETSC_FALSE, &i, &odi, &odj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot restore IJ structure");
  PetscCall(MatRestoreRowIJ(Ao, 0, PETSC_FALSE, PETSC_FALSE, &i, &ooi, &ooj, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot restore IJ structure");
  PetscCall(MatSeqAIJRestoreArray(Ad, &dd));
  PetscCall(MatSeqAIJRestoreArray(Ao, &od));

  ii = aux;
  jj = aux + dr + 1;
  aa = data;
  PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, dr, lc, ii, jj, aa, &lA));

  /* create containers to destroy the data */
  ptrs[0] = aux;
  ptrs[1] = data;
  for (i = 0; i < 2; i++) PetscCall(PetscObjectContainerCompose((PetscObject)lA, names[i], ptrs[i], PetscCtxDestroyDefault));
  if (ismpibaij) { /* destroy converted local matrices */
    PetscCall(MatDestroy(&Ad));
    PetscCall(MatDestroy(&Ao));
  }

  /* finalize matrix */
  PetscCall(MatISSetLocalMat(B, lA));
  PetscCall(MatDestroy(&lA));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &B));
  else *newmat = B;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatConvert_Nest_IS(Mat A, MatType type, MatReuse reuse, Mat *newmat)
{
  Mat                  **nest, *snest, **rnest, lA, B;
  IS                    *iscol, *isrow, *islrow, *islcol;
  ISLocalToGlobalMapping rl2g, cl2g;
  MPI_Comm               comm;
  PetscInt              *lr, *lc, *l2gidxs;
  PetscInt               i, j, nr, nc, rbs, cbs;
  PetscBool              convert, lreuse, *istrans;
  PetscBool3             allow_repeated = PETSC_BOOL3_UNKNOWN;

  PetscFunctionBegin;
  PetscCall(MatNestGetSubMats(A, &nr, &nc, &nest));
  lreuse = PETSC_FALSE;
  rnest  = NULL;
  if (reuse == MAT_REUSE_MATRIX) {
    PetscBool ismatis, isnest;

    PetscCall(PetscObjectTypeCompare((PetscObject)*newmat, MATIS, &ismatis));
    PetscCheck(ismatis, PetscObjectComm((PetscObject)*newmat), PETSC_ERR_USER, "Cannot reuse matrix of type %s", ((PetscObject)*newmat)->type_name);
    PetscCall(MatISGetLocalMat(*newmat, &lA));
    PetscCall(PetscObjectTypeCompare((PetscObject)lA, MATNEST, &isnest));
    if (isnest) {
      PetscCall(MatNestGetSubMats(lA, &i, &j, &rnest));
      lreuse = (PetscBool)(i == nr && j == nc);
      if (!lreuse) rnest = NULL;
    }
  }
  PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
  PetscCall(PetscCalloc2(nr, &lr, nc, &lc));
  PetscCall(PetscCalloc6(nr, &isrow, nc, &iscol, nr, &islrow, nc, &islcol, nr * nc, &snest, nr * nc, &istrans));
  PetscCall(MatNestGetISs(A, isrow, iscol));
  for (i = 0; i < nr; i++) {
    for (j = 0; j < nc; j++) {
      PetscBool ismatis, sallow;
      PetscInt  l1, l2, lb1, lb2, ij = i * nc + j;

      /* Null matrix pointers are allowed in MATNEST */
      if (!nest[i][j]) continue;

      /* Nested matrices should be of type MATIS */
      PetscCall(PetscObjectTypeCompare((PetscObject)nest[i][j], MATTRANSPOSEVIRTUAL, &istrans[ij]));
      if (istrans[ij]) {
        Mat T, lT;
        PetscCall(MatTransposeGetMat(nest[i][j], &T));
        PetscCall(PetscObjectTypeCompare((PetscObject)T, MATIS, &ismatis));
        PetscCheck(ismatis, comm, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") (transposed) is not of type MATIS", i, j);
        PetscCall(MatISGetAllowRepeated(T, &sallow));
        PetscCall(MatISGetLocalMat(T, &lT));
        PetscCall(MatCreateTranspose(lT, &snest[ij]));
      } else {
        PetscCall(PetscObjectTypeCompare((PetscObject)nest[i][j], MATIS, &ismatis));
        PetscCheck(ismatis, comm, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") is not of type MATIS", i, j);
        PetscCall(MatISGetAllowRepeated(nest[i][j], &sallow));
        PetscCall(MatISGetLocalMat(nest[i][j], &snest[ij]));
      }
      if (allow_repeated == PETSC_BOOL3_UNKNOWN) allow_repeated = PetscBoolToBool3(sallow);
      PetscCheck(sallow == PetscBool3ToBool(allow_repeated), comm, PETSC_ERR_SUP, "Cannot mix repeated and non repeated maps");

      /* Check compatibility of local sizes */
      PetscCall(MatGetSize(snest[ij], &l1, &l2));
      PetscCall(MatGetBlockSizes(snest[ij], &lb1, &lb2));
      if (!l1 || !l2) continue;
      PetscCheck(!lr[i] || l1 == lr[i], PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid local size %" PetscInt_FMT " != %" PetscInt_FMT, i, j, lr[i], l1);
      PetscCheck(!lc[j] || l2 == lc[j], PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid local size %" PetscInt_FMT " != %" PetscInt_FMT, i, j, lc[j], l2);
      lr[i] = l1;
      lc[j] = l2;

      /* check compatibility for local matrix reusage */
      if (rnest && !rnest[i][j] != !snest[ij]) lreuse = PETSC_FALSE;
    }
  }

  if (PetscDefined(USE_DEBUG)) {
    /* Check compatibility of l2g maps for rows */
    for (i = 0; i < nr; i++) {
      rl2g = NULL;
      for (j = 0; j < nc; j++) {
        PetscInt n1, n2;

        if (!nest[i][j]) continue;
        if (istrans[i * nc + j]) {
          Mat T;

          PetscCall(MatTransposeGetMat(nest[i][j], &T));
          PetscCall(MatISGetLocalToGlobalMapping(T, NULL, &cl2g));
        } else {
          PetscCall(MatISGetLocalToGlobalMapping(nest[i][j], &cl2g, NULL));
        }
        PetscCall(ISLocalToGlobalMappingGetSize(cl2g, &n1));
        if (!n1) continue;
        if (!rl2g) {
          rl2g = cl2g;
        } else {
          const PetscInt *idxs1, *idxs2;
          PetscBool       same;

          PetscCall(ISLocalToGlobalMappingGetSize(rl2g, &n2));
          PetscCheck(n1 == n2, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid row l2gmap size %" PetscInt_FMT " != %" PetscInt_FMT, i, j, n1, n2);
          PetscCall(ISLocalToGlobalMappingGetIndices(cl2g, &idxs1));
          PetscCall(ISLocalToGlobalMappingGetIndices(rl2g, &idxs2));
          PetscCall(PetscArraycmp(idxs1, idxs2, n1, &same));
          PetscCall(ISLocalToGlobalMappingRestoreIndices(cl2g, &idxs1));
          PetscCall(ISLocalToGlobalMappingRestoreIndices(rl2g, &idxs2));
          PetscCheck(same, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid row l2gmap", i, j);
        }
      }
    }
    /* Check compatibility of l2g maps for columns */
    for (i = 0; i < nc; i++) {
      rl2g = NULL;
      for (j = 0; j < nr; j++) {
        PetscInt n1, n2;

        if (!nest[j][i]) continue;
        if (istrans[j * nc + i]) {
          Mat T;

          PetscCall(MatTransposeGetMat(nest[j][i], &T));
          PetscCall(MatISGetLocalToGlobalMapping(T, &cl2g, NULL));
        } else {
          PetscCall(MatISGetLocalToGlobalMapping(nest[j][i], NULL, &cl2g));
        }
        PetscCall(ISLocalToGlobalMappingGetSize(cl2g, &n1));
        if (!n1) continue;
        if (!rl2g) {
          rl2g = cl2g;
        } else {
          const PetscInt *idxs1, *idxs2;
          PetscBool       same;

          PetscCall(ISLocalToGlobalMappingGetSize(rl2g, &n2));
          PetscCheck(n1 == n2, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid column l2gmap size %" PetscInt_FMT " != %" PetscInt_FMT, j, i, n1, n2);
          PetscCall(ISLocalToGlobalMappingGetIndices(cl2g, &idxs1));
          PetscCall(ISLocalToGlobalMappingGetIndices(rl2g, &idxs2));
          PetscCall(PetscArraycmp(idxs1, idxs2, n1, &same));
          PetscCall(ISLocalToGlobalMappingRestoreIndices(cl2g, &idxs1));
          PetscCall(ISLocalToGlobalMappingRestoreIndices(rl2g, &idxs2));
          PetscCheck(same, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot convert from MATNEST to MATIS! Matrix block (%" PetscInt_FMT ",%" PetscInt_FMT ") has invalid column l2gmap", j, i);
        }
      }
    }
  }

  B = NULL;
  if (reuse != MAT_REUSE_MATRIX) {
    PetscInt stl;

    /* Create l2g map for the rows of the new matrix and index sets for the local MATNEST */
    for (i = 0, stl = 0; i < nr; i++) stl += lr[i];
    PetscCall(PetscMalloc1(stl, &l2gidxs));
    for (i = 0, stl = 0; i < nr; i++) {
      Mat             usedmat;
      Mat_IS         *matis;
      const PetscInt *idxs;

      /* local IS for local NEST */
      PetscCall(ISCreateStride(PETSC_COMM_SELF, lr[i], stl, 1, &islrow[i]));

      /* l2gmap */
      j       = 0;
      usedmat = nest[i][j];
      while (!usedmat && j < nc - 1) usedmat = nest[i][++j];
      PetscCheck(usedmat, comm, PETSC_ERR_SUP, "Cannot find valid row mat");

      if (istrans[i * nc + j]) {
        Mat T;
        PetscCall(MatTransposeGetMat(usedmat, &T));
        usedmat = T;
      }
      matis = (Mat_IS *)usedmat->data;
      PetscCall(ISGetIndices(isrow[i], &idxs));
      if (istrans[i * nc + j]) {
        PetscCall(PetscSFBcastBegin(matis->csf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(matis->csf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
      } else {
        PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
      }
      PetscCall(ISRestoreIndices(isrow[i], &idxs));
      stl += lr[i];
    }
    PetscCall(ISLocalToGlobalMappingCreate(comm, 1, stl, l2gidxs, PETSC_OWN_POINTER, &rl2g));

    /* Create l2g map for columns of the new matrix and index sets for the local MATNEST */
    for (i = 0, stl = 0; i < nc; i++) stl += lc[i];
    PetscCall(PetscMalloc1(stl, &l2gidxs));
    for (i = 0, stl = 0; i < nc; i++) {
      Mat             usedmat;
      Mat_IS         *matis;
      const PetscInt *idxs;

      /* local IS for local NEST */
      PetscCall(ISCreateStride(PETSC_COMM_SELF, lc[i], stl, 1, &islcol[i]));

      /* l2gmap */
      j       = 0;
      usedmat = nest[j][i];
      while (!usedmat && j < nr - 1) usedmat = nest[++j][i];
      PetscCheck(usedmat, comm, PETSC_ERR_SUP, "Cannot find valid column mat");
      if (istrans[j * nc + i]) {
        Mat T;
        PetscCall(MatTransposeGetMat(usedmat, &T));
        usedmat = T;
      }
      matis = (Mat_IS *)usedmat->data;
      PetscCall(ISGetIndices(iscol[i], &idxs));
      if (istrans[j * nc + i]) {
        PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
      } else {
        PetscCall(PetscSFBcastBegin(matis->csf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
        PetscCall(PetscSFBcastEnd(matis->csf, MPIU_INT, idxs, l2gidxs + stl, MPI_REPLACE));
      }
      PetscCall(ISRestoreIndices(iscol[i], &idxs));
      stl += lc[i];
    }
    PetscCall(ISLocalToGlobalMappingCreate(comm, 1, stl, l2gidxs, PETSC_OWN_POINTER, &cl2g));

    /* Create MATIS */
    PetscCall(MatCreate(comm, &B));
    PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    PetscCall(MatGetBlockSizes(A, &rbs, &cbs));
    PetscCall(MatSetBlockSizes(B, rbs, cbs));
    PetscCall(MatSetType(B, MATIS));
    PetscCall(MatISSetLocalMatType(B, MATNEST));
    PetscCall(MatISSetAllowRepeated(B, PetscBool3ToBool(allow_repeated)));
    { /* hack : avoid setup of scatters */
      Mat_IS *matis     = (Mat_IS *)B->data;
      matis->islocalref = B;
    }
    PetscCall(MatSetLocalToGlobalMapping(B, rl2g, cl2g));
    PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
    PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
    PetscCall(MatCreateNest(PETSC_COMM_SELF, nr, islrow, nc, islcol, snest, &lA));
    PetscCall(MatNestSetVecType(lA, VECNEST));
    for (i = 0; i < nr * nc; i++) {
      if (istrans[i]) PetscCall(MatDestroy(&snest[i]));
    }
    PetscCall(MatISSetLocalMat(B, lA));
    PetscCall(MatDestroy(&lA));
    { /* hack : setup of scatters done here */
      Mat_IS *matis = (Mat_IS *)B->data;

      matis->islocalref = NULL;
      PetscCall(MatISSetUpScatters_Private(B));
    }
    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    if (reuse == MAT_INPLACE_MATRIX) {
      PetscCall(MatHeaderReplace(A, &B));
    } else {
      *newmat = B;
    }
  } else {
    if (lreuse) {
      PetscCall(MatISGetLocalMat(*newmat, &lA));
      for (i = 0; i < nr; i++) {
        for (j = 0; j < nc; j++) {
          if (snest[i * nc + j]) {
            PetscCall(MatNestSetSubMat(lA, i, j, snest[i * nc + j]));
            if (istrans[i * nc + j]) PetscCall(MatDestroy(&snest[i * nc + j]));
          }
        }
      }
    } else {
      PetscInt stl;
      for (i = 0, stl = 0; i < nr; i++) {
        PetscCall(ISCreateStride(PETSC_COMM_SELF, lr[i], stl, 1, &islrow[i]));
        stl += lr[i];
      }
      for (i = 0, stl = 0; i < nc; i++) {
        PetscCall(ISCreateStride(PETSC_COMM_SELF, lc[i], stl, 1, &islcol[i]));
        stl += lc[i];
      }
      PetscCall(MatCreateNest(PETSC_COMM_SELF, nr, islrow, nc, islcol, snest, &lA));
      for (i = 0; i < nr * nc; i++) {
        if (istrans[i]) PetscCall(MatDestroy(&snest[i]));
      }
      PetscCall(MatISSetLocalMat(*newmat, lA));
      PetscCall(MatDestroy(&lA));
    }
    PetscCall(MatAssemblyBegin(*newmat, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(*newmat, MAT_FINAL_ASSEMBLY));
  }

  /* Create local matrix in MATNEST format */
  convert = PETSC_FALSE;
  PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)A)->prefix, "-mat_is_convert_local_nest", &convert, NULL));
  if (convert) {
    Mat              M;
    MatISLocalFields lf;

    PetscCall(MatISGetLocalMat(*newmat, &lA));
    PetscCall(MatConvert(lA, MATAIJ, MAT_INITIAL_MATRIX, &M));
    PetscCall(MatISSetLocalMat(*newmat, M));
    PetscCall(MatDestroy(&M));

    /* attach local fields to the matrix */
    PetscCall(PetscNew(&lf));
    PetscCall(PetscMalloc2(nr, &lf->rf, nc, &lf->cf));
    for (i = 0; i < nr; i++) {
      PetscInt n, st;

      PetscCall(ISGetLocalSize(islrow[i], &n));
      PetscCall(ISStrideGetInfo(islrow[i], &st, NULL));
      PetscCall(ISCreateStride(comm, n, st, 1, &lf->rf[i]));
    }
    for (i = 0; i < nc; i++) {
      PetscInt n, st;

      PetscCall(ISGetLocalSize(islcol[i], &n));
      PetscCall(ISStrideGetInfo(islcol[i], &st, NULL));
      PetscCall(ISCreateStride(comm, n, st, 1, &lf->cf[i]));
    }
    lf->nr = nr;
    lf->nc = nc;
    PetscCall(PetscObjectContainerCompose((PetscObject)*newmat, "_convert_nest_lfields", lf, MatISContainerDestroyFields_Private));
  }

  /* Free workspace */
  for (i = 0; i < nr; i++) PetscCall(ISDestroy(&islrow[i]));
  for (i = 0; i < nc; i++) PetscCall(ISDestroy(&islcol[i]));
  PetscCall(PetscFree6(isrow, iscol, islrow, islcol, snest, istrans));
  PetscCall(PetscFree2(lr, lc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDiagonalScale_IS(Mat A, Vec l, Vec r)
{
  Mat_IS            *matis = (Mat_IS *)A->data;
  Vec                ll, rr;
  const PetscScalar *Y, *X;
  PetscScalar       *x, *y;

  PetscFunctionBegin;
  if (l) {
    ll = matis->y;
    PetscCall(VecGetArrayRead(l, &Y));
    PetscCall(VecGetArray(ll, &y));
    PetscCall(PetscSFBcastBegin(matis->sf, MPIU_SCALAR, Y, y, MPI_REPLACE));
  } else {
    ll = NULL;
  }
  if (r) {
    rr = matis->x;
    PetscCall(VecGetArrayRead(r, &X));
    PetscCall(VecGetArray(rr, &x));
    PetscCall(PetscSFBcastBegin(matis->csf, MPIU_SCALAR, X, x, MPI_REPLACE));
  } else {
    rr = NULL;
  }
  if (ll) {
    PetscCall(PetscSFBcastEnd(matis->sf, MPIU_SCALAR, Y, y, MPI_REPLACE));
    PetscCall(VecRestoreArrayRead(l, &Y));
    PetscCall(VecRestoreArray(ll, &y));
  }
  if (rr) {
    PetscCall(PetscSFBcastEnd(matis->csf, MPIU_SCALAR, X, x, MPI_REPLACE));
    PetscCall(VecRestoreArrayRead(r, &X));
    PetscCall(VecRestoreArray(rr, &x));
  }
  PetscCall(MatDiagonalScale(matis->A, ll, rr));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetInfo_IS(Mat A, MatInfoType flag, MatInfo *ginfo)
{
  Mat_IS        *matis = (Mat_IS *)A->data;
  MatInfo        info;
  PetscLogDouble isend[6], irecv[6];
  PetscInt       bs;

  PetscFunctionBegin;
  PetscCall(MatGetBlockSize(A, &bs));
  if (matis->A->ops->getinfo) {
    PetscCall(MatGetInfo(matis->A, MAT_LOCAL, &info));
    isend[0] = info.nz_used;
    isend[1] = info.nz_allocated;
    isend[2] = info.nz_unneeded;
    isend[3] = info.memory;
    isend[4] = info.mallocs;
  } else {
    isend[0] = 0.;
    isend[1] = 0.;
    isend[2] = 0.;
    isend[3] = 0.;
    isend[4] = 0.;
  }
  isend[5] = matis->A->num_ass;
  if (flag == MAT_LOCAL) {
    ginfo->nz_used      = isend[0];
    ginfo->nz_allocated = isend[1];
    ginfo->nz_unneeded  = isend[2];
    ginfo->memory       = isend[3];
    ginfo->mallocs      = isend[4];
    ginfo->assemblies   = isend[5];
  } else if (flag == MAT_GLOBAL_MAX) {
    PetscCallMPI(MPIU_Allreduce(isend, irecv, 6, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)A)));

    ginfo->nz_used      = irecv[0];
    ginfo->nz_allocated = irecv[1];
    ginfo->nz_unneeded  = irecv[2];
    ginfo->memory       = irecv[3];
    ginfo->mallocs      = irecv[4];
    ginfo->assemblies   = irecv[5];
  } else if (flag == MAT_GLOBAL_SUM) {
    PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)A)));

    ginfo->nz_used      = irecv[0];
    ginfo->nz_allocated = irecv[1];
    ginfo->nz_unneeded  = irecv[2];
    ginfo->memory       = irecv[3];
    ginfo->mallocs      = irecv[4];
    ginfo->assemblies   = A->num_ass;
  }
  ginfo->block_size        = bs;
  ginfo->fill_ratio_given  = 0;
  ginfo->fill_ratio_needed = 0;
  ginfo->factor_mallocs    = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatTranspose_IS(Mat A, MatReuse reuse, Mat *B)
{
  Mat C, lC, lA;

  PetscFunctionBegin;
  if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
    ISLocalToGlobalMapping rl2g, cl2g;
    PetscBool              allow_repeated;

    PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    PetscCall(MatSetSizes(C, A->cmap->n, A->rmap->n, A->cmap->N, A->rmap->N));
    PetscCall(MatSetBlockSizes(C, A->cmap->bs, A->rmap->bs));
    PetscCall(MatSetType(C, MATIS));
    PetscCall(MatISGetAllowRepeated(A, &allow_repeated));
    PetscCall(MatISSetAllowRepeated(C, allow_repeated));
    PetscCall(MatGetLocalToGlobalMapping(A, &rl2g, &cl2g));
    PetscCall(MatSetLocalToGlobalMapping(C, cl2g, rl2g));
  } else C = *B;

  /* perform local transposition */
  PetscCall(MatISGetLocalMat(A, &lA));
  PetscCall(MatTranspose(lA, MAT_INITIAL_MATRIX, &lC));
  PetscCall(MatSetLocalToGlobalMapping(lC, lA->cmap->mapping, lA->rmap->mapping));
  PetscCall(MatISSetLocalMat(C, lC));
  PetscCall(MatDestroy(&lC));

  if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    *B = C;
  } else {
    PetscCall(MatHeaderMerge(A, &C));
  }
  PetscCall(MatAssemblyBegin(*B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*B, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDiagonalSet_IS(Mat A, Vec D, InsertMode insmode)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCheck(!is->allow_repeated || insmode == ADD_VALUES, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "INSERT_VALUES with repeated entries not supported");
  if (D) { /* MatShift_IS pass D = NULL */
    PetscCall(VecScatterBegin(is->rctx, D, is->y, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(is->rctx, D, is->y, INSERT_VALUES, SCATTER_FORWARD));
  }
  PetscCall(VecPointwiseDivide(is->y, is->y, is->counter));
  PetscCall(MatDiagonalSet(is->A, is->y, insmode));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatShift_IS(Mat A, PetscScalar a)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(VecSet(is->y, a));
  PetscCall(MatDiagonalSet_IS(A, NULL, ADD_VALUES));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesLocal_SubMat_IS(Mat A, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  PetscInt buf[2 * MATIS_MAX_ENTRIES_INSERTION], *rows_l = NULL, *cols_l = NULL;

  PetscFunctionBegin;
  IndexSpaceGet(buf, m, n, rows_l, cols_l);
  PetscCall(ISLocalToGlobalMappingApply(A->rmap->mapping, m, rows, rows_l));
  PetscCall(ISLocalToGlobalMappingApply(A->cmap->mapping, n, cols, cols_l));
  PetscCall(MatSetValuesLocal_IS(A, m, rows_l, n, cols_l, values, addv));
  IndexSpaceRestore(buf, m, n, rows_l, cols_l);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesBlockedLocal_SubMat_IS(Mat A, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  PetscInt buf[2 * MATIS_MAX_ENTRIES_INSERTION], *rows_l = NULL, *cols_l = NULL, rbs, cbs;

  PetscFunctionBegin;
  /* We cannot guarantee the local matrix will have the same block size of the original matrix */
  PetscCall(ISLocalToGlobalMappingGetBlockSize(A->rmap->mapping, &rbs));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(A->cmap->mapping, &cbs));
  IndexSpaceGet(buf, m * rbs, n * cbs, rows_l, cols_l);
  BlockIndicesExpand(m, rows, rbs, rows_l);
  BlockIndicesExpand(n, cols, cbs, cols_l);
  PetscCall(ISLocalToGlobalMappingApply(A->rmap->mapping, m * rbs, rows_l, rows_l));
  PetscCall(ISLocalToGlobalMappingApply(A->cmap->mapping, n * cbs, cols_l, cols_l));
  PetscCall(MatSetValuesLocal_IS(A, m * rbs, rows_l, n * cbs, cols_l, values, addv));
  IndexSpaceRestore(buf, m * rbs, n * cbs, rows_l, cols_l);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsLocal_SubMat_IS(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  PetscInt *rows_l;
  Mat_IS   *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(n, &rows_l));
  PetscCall(ISLocalToGlobalMappingApply(A->rmap->mapping, n, rows, rows_l));
  PetscCall(MatZeroRowsLocal(is->islocalref, n, rows_l, diag, x, b));
  PetscCall(PetscFree(rows_l));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsColumnsLocal_SubMat_IS(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  PetscInt *rows_l;
  Mat_IS   *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(n, &rows_l));
  PetscCall(ISLocalToGlobalMappingApply(A->rmap->mapping, n, rows, rows_l));
  PetscCall(MatZeroRowsColumnsLocal(is->islocalref, n, rows_l, diag, x, b));
  PetscCall(PetscFree(rows_l));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatrix_IS(Mat mat, IS irow, IS icol, MatReuse scall, Mat *newmat)
{
  Mat             locmat, newlocmat;
  Mat_IS         *newmatis;
  const PetscInt *idxs;
  PetscInt        i, m, n;

  PetscFunctionBegin;
  if (scall == MAT_REUSE_MATRIX) {
    PetscBool ismatis;

    PetscCall(PetscObjectTypeCompare((PetscObject)*newmat, MATIS, &ismatis));
    PetscCheck(ismatis, PetscObjectComm((PetscObject)*newmat), PETSC_ERR_ARG_WRONG, "Cannot reuse matrix! Not of MATIS type");
    newmatis = (Mat_IS *)(*newmat)->data;
    PetscCheck(newmatis->getsub_ris, PetscObjectComm((PetscObject)*newmat), PETSC_ERR_ARG_WRONG, "Cannot reuse matrix! Misses local row IS");
    PetscCheck(newmatis->getsub_cis, PetscObjectComm((PetscObject)*newmat), PETSC_ERR_ARG_WRONG, "Cannot reuse matrix! Misses local col IS");
  }
  /* irow and icol may not have duplicate entries */
  if (PetscDefined(USE_DEBUG)) {
    Vec                rtest, ltest;
    const PetscScalar *array;

    PetscCall(MatCreateVecs(mat, &ltest, &rtest));
    PetscCall(ISGetLocalSize(irow, &n));
    PetscCall(ISGetIndices(irow, &idxs));
    for (i = 0; i < n; i++) PetscCall(VecSetValue(rtest, idxs[i], 1.0, ADD_VALUES));
    PetscCall(VecAssemblyBegin(rtest));
    PetscCall(VecAssemblyEnd(rtest));
    PetscCall(VecGetLocalSize(rtest, &n));
    PetscCall(VecGetOwnershipRange(rtest, &m, NULL));
    PetscCall(VecGetArrayRead(rtest, &array));
    for (i = 0; i < n; i++) PetscCheck(array[i] == 0. || array[i] == 1., PETSC_COMM_SELF, PETSC_ERR_SUP, "Index %" PetscInt_FMT " counted %" PetscInt_FMT " times! Irow may not have duplicate entries", i + m, (PetscInt)PetscRealPart(array[i]));
    PetscCall(VecRestoreArrayRead(rtest, &array));
    PetscCall(ISRestoreIndices(irow, &idxs));
    PetscCall(ISGetLocalSize(icol, &n));
    PetscCall(ISGetIndices(icol, &idxs));
    for (i = 0; i < n; i++) PetscCall(VecSetValue(ltest, idxs[i], 1.0, ADD_VALUES));
    PetscCall(VecAssemblyBegin(ltest));
    PetscCall(VecAssemblyEnd(ltest));
    PetscCall(VecGetLocalSize(ltest, &n));
    PetscCall(VecGetOwnershipRange(ltest, &m, NULL));
    PetscCall(VecGetArrayRead(ltest, &array));
    for (i = 0; i < n; i++) PetscCheck(array[i] == 0. || array[i] == 1., PETSC_COMM_SELF, PETSC_ERR_SUP, "Index %" PetscInt_FMT " counted %" PetscInt_FMT " times! Icol may not have duplicate entries", i + m, (PetscInt)PetscRealPart(array[i]));
    PetscCall(VecRestoreArrayRead(ltest, &array));
    PetscCall(ISRestoreIndices(icol, &idxs));
    PetscCall(VecDestroy(&rtest));
    PetscCall(VecDestroy(&ltest));
  }
  if (scall == MAT_INITIAL_MATRIX) {
    Mat_IS                *matis = (Mat_IS *)mat->data;
    ISLocalToGlobalMapping rl2g;
    IS                     is;
    PetscInt              *lidxs, *lgidxs, *newgidxs;
    PetscInt               ll, newloc, irbs, icbs, arbs, acbs, rbs, cbs;
    PetscBool              cong;
    MPI_Comm               comm;

    PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    PetscCall(MatGetBlockSizes(mat, &arbs, &acbs));
    PetscCall(ISGetBlockSize(irow, &irbs));
    PetscCall(ISGetBlockSize(icol, &icbs));
    rbs = arbs == irbs ? irbs : 1;
    cbs = acbs == icbs ? icbs : 1;
    PetscCall(ISGetLocalSize(irow, &m));
    PetscCall(ISGetLocalSize(icol, &n));
    PetscCall(MatCreate(comm, newmat));
    PetscCall(MatSetType(*newmat, MATIS));
    PetscCall(MatISSetAllowRepeated(*newmat, matis->allow_repeated));
    PetscCall(MatSetSizes(*newmat, m, n, PETSC_DECIDE, PETSC_DECIDE));
    PetscCall(MatSetBlockSizes(*newmat, rbs, cbs));
    /* communicate irow to their owners in the layout */
    PetscCall(ISGetIndices(irow, &idxs));
    PetscCall(PetscLayoutMapLocal(mat->rmap, m, idxs, &ll, &lidxs, &lgidxs));
    PetscCall(ISRestoreIndices(irow, &idxs));
    PetscCall(PetscArrayzero(matis->sf_rootdata, matis->sf->nroots));
    for (i = 0; i < ll; i++) matis->sf_rootdata[lidxs[i]] = lgidxs[i] + 1;
    PetscCall(PetscFree(lidxs));
    PetscCall(PetscFree(lgidxs));
    PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
    PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
    for (i = 0, newloc = 0; i < matis->sf->nleaves; i++)
      if (matis->sf_leafdata[i]) newloc++;
    PetscCall(PetscMalloc1(newloc, &newgidxs));
    PetscCall(PetscMalloc1(newloc, &lidxs));
    for (i = 0, newloc = 0; i < matis->sf->nleaves; i++)
      if (matis->sf_leafdata[i]) {
        lidxs[newloc]      = i;
        newgidxs[newloc++] = matis->sf_leafdata[i] - 1;
      }
    PetscCall(ISCreateGeneral(comm, newloc, newgidxs, PETSC_OWN_POINTER, &is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &rl2g));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(rl2g, rbs));
    PetscCall(ISDestroy(&is));
    /* local is to extract local submatrix */
    newmatis = (Mat_IS *)(*newmat)->data;
    PetscCall(ISCreateGeneral(comm, newloc, lidxs, PETSC_OWN_POINTER, &newmatis->getsub_ris));
    PetscCall(MatHasCongruentLayouts(mat, &cong));
    if (cong && irow == icol && matis->csf == matis->sf) {
      PetscCall(MatSetLocalToGlobalMapping(*newmat, rl2g, rl2g));
      PetscCall(PetscObjectReference((PetscObject)newmatis->getsub_ris));
      newmatis->getsub_cis = newmatis->getsub_ris;
    } else {
      ISLocalToGlobalMapping cl2g;

      /* communicate icol to their owners in the layout */
      PetscCall(ISGetIndices(icol, &idxs));
      PetscCall(PetscLayoutMapLocal(mat->cmap, n, idxs, &ll, &lidxs, &lgidxs));
      PetscCall(ISRestoreIndices(icol, &idxs));
      PetscCall(PetscArrayzero(matis->csf_rootdata, matis->csf->nroots));
      for (i = 0; i < ll; i++) matis->csf_rootdata[lidxs[i]] = lgidxs[i] + 1;
      PetscCall(PetscFree(lidxs));
      PetscCall(PetscFree(lgidxs));
      PetscCall(PetscSFBcastBegin(matis->csf, MPIU_INT, matis->csf_rootdata, matis->csf_leafdata, MPI_REPLACE));
      PetscCall(PetscSFBcastEnd(matis->csf, MPIU_INT, matis->csf_rootdata, matis->csf_leafdata, MPI_REPLACE));
      for (i = 0, newloc = 0; i < matis->csf->nleaves; i++)
        if (matis->csf_leafdata[i]) newloc++;
      PetscCall(PetscMalloc1(newloc, &newgidxs));
      PetscCall(PetscMalloc1(newloc, &lidxs));
      for (i = 0, newloc = 0; i < matis->csf->nleaves; i++)
        if (matis->csf_leafdata[i]) {
          lidxs[newloc]      = i;
          newgidxs[newloc++] = matis->csf_leafdata[i] - 1;
        }
      PetscCall(ISCreateGeneral(comm, newloc, newgidxs, PETSC_OWN_POINTER, &is));
      PetscCall(ISLocalToGlobalMappingCreateIS(is, &cl2g));
      PetscCall(ISLocalToGlobalMappingSetBlockSize(cl2g, cbs));
      PetscCall(ISDestroy(&is));
      /* local is to extract local submatrix */
      PetscCall(ISCreateGeneral(comm, newloc, lidxs, PETSC_OWN_POINTER, &newmatis->getsub_cis));
      PetscCall(MatSetLocalToGlobalMapping(*newmat, rl2g, cl2g));
      PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
    }
    PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
  } else {
    PetscCall(MatISGetLocalMat(*newmat, &newlocmat));
  }
  PetscCall(MatISGetLocalMat(mat, &locmat));
  newmatis = (Mat_IS *)(*newmat)->data;
  PetscCall(MatCreateSubMatrix(locmat, newmatis->getsub_ris, newmatis->getsub_cis, scall, &newlocmat));
  if (scall == MAT_INITIAL_MATRIX) {
    PetscCall(MatISSetLocalMat(*newmat, newlocmat));
    PetscCall(MatDestroy(&newlocmat));
  }
  PetscCall(MatAssemblyBegin(*newmat, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(*newmat, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCopy_IS(Mat A, Mat B, MatStructure str)
{
  Mat_IS   *a = (Mat_IS *)A->data, *b;
  PetscBool ismatis;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)B, MATIS, &ismatis));
  PetscCheck(ismatis, PetscObjectComm((PetscObject)B), PETSC_ERR_SUP, "Need to be implemented");
  b = (Mat_IS *)B->data;
  PetscCall(MatCopy(a->A, b->A, str));
  PetscCall(PetscObjectStateIncrease((PetscObject)B));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMissingDiagonal_IS(Mat A, PetscBool *missing, PetscInt *d)
{
  Vec                v;
  const PetscScalar *array;
  PetscInt           i, n;

  PetscFunctionBegin;
  *missing = PETSC_FALSE;
  PetscCall(MatCreateVecs(A, NULL, &v));
  PetscCall(MatGetDiagonal(A, v));
  PetscCall(VecGetLocalSize(v, &n));
  PetscCall(VecGetArrayRead(v, &array));
  for (i = 0; i < n; i++)
    if (array[i] == 0.) break;
  PetscCall(VecRestoreArrayRead(v, &array));
  PetscCall(VecDestroy(&v));
  if (i != n) *missing = PETSC_TRUE;
  if (d) {
    *d = -1;
    if (*missing) {
      PetscInt rstart;
      PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
      *d = i + rstart;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetUpSF_IS(Mat B)
{
  Mat_IS         *matis = (Mat_IS *)B->data;
  const PetscInt *gidxs;
  PetscInt        nleaves;

  PetscFunctionBegin;
  if (matis->sf) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)B), &matis->sf));
  PetscCall(ISLocalToGlobalMappingGetIndices(matis->rmapping, &gidxs));
  PetscCall(ISLocalToGlobalMappingGetSize(matis->rmapping, &nleaves));
  PetscCall(PetscSFSetGraphLayout(matis->sf, B->rmap, nleaves, NULL, PETSC_OWN_POINTER, gidxs));
  PetscCall(ISLocalToGlobalMappingRestoreIndices(matis->rmapping, &gidxs));
  PetscCall(PetscMalloc2(matis->sf->nroots, &matis->sf_rootdata, matis->sf->nleaves, &matis->sf_leafdata));
  if (matis->rmapping != matis->cmapping) { /* setup SF for columns */
    PetscCall(ISLocalToGlobalMappingGetSize(matis->cmapping, &nleaves));
    PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)B), &matis->csf));
    PetscCall(ISLocalToGlobalMappingGetIndices(matis->cmapping, &gidxs));
    PetscCall(PetscSFSetGraphLayout(matis->csf, B->cmap, nleaves, NULL, PETSC_OWN_POINTER, gidxs));
    PetscCall(ISLocalToGlobalMappingRestoreIndices(matis->cmapping, &gidxs));
    PetscCall(PetscMalloc2(matis->csf->nroots, &matis->csf_rootdata, matis->csf->nleaves, &matis->csf_leafdata));
  } else {
    matis->csf          = matis->sf;
    matis->csf_leafdata = matis->sf_leafdata;
    matis->csf_rootdata = matis->sf_rootdata;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISGetAllowRepeated - Get the flag to allow repeated entries in the local to global map

  Not Collective

  Input Parameter:
. A - the matrix

  Output Parameter:
. flg - the boolean flag

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateIS()`, `MatSetLocalToGlobalMapping()`, `MatISSetAllowRepeated()`
@*/
PetscErrorCode MatISGetAllowRepeated(Mat A, PetscBool *flg)
{
  PetscBool ismatis;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscAssertPointer(flg, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATIS, &ismatis));
  PetscCheck(ismatis, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for matrix type %s", ((PetscObject)A)->type_name);
  *flg = ((Mat_IS *)A->data)->allow_repeated;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISSetAllowRepeated - Set the flag to allow repeated entries in the local to global map

  Logically Collective

  Input Parameters:
+ A   - the matrix
- flg - the boolean flag

  Level: intermediate

  Notes:
  The default value is `PETSC_FALSE`.
  When called AFTER calling `MatSetLocalToGlobalMapping()` it will recreate the local matrices
  if `flg` is different from the previously set value.
  Specifically, when `flg` is true it will just recreate the local matrices, while if
  `flg` is false will assemble the local matrices summing up repeated entries.

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateIS()`, `MatSetLocalToGlobalMapping()`, `MatISGetAllowRepeated()`
@*/
PetscErrorCode MatISSetAllowRepeated(Mat A, PetscBool flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscValidLogicalCollectiveBool(A, flg, 2);
  PetscTryMethod(A, "MatISSetAllowRepeated_C", (Mat, PetscBool), (A, flg));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetAllowRepeated_IS(Mat A, PetscBool flg)
{
  Mat_IS                *matis = (Mat_IS *)A->data;
  Mat                    lA    = NULL;
  ISLocalToGlobalMapping lrmap, lcmap;

  PetscFunctionBegin;
  if (flg == matis->allow_repeated) PetscFunctionReturn(PETSC_SUCCESS);
  if (!matis->A) { /* matrix has not been preallocated yet */
    matis->allow_repeated = flg;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCheck(!matis->islocalref, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not implemented for local references");
  if (matis->allow_repeated) { /* we will assemble the old local matrix if needed */
    lA = matis->A;
    PetscCall(PetscObjectReference((PetscObject)lA));
  }
  /* In case flg is True, we only recreate the local matrix */
  matis->allow_repeated = flg;
  PetscCall(MatSetLocalToGlobalMapping(A, A->rmap->mapping, A->cmap->mapping));
  if (lA) { /* assemble previous local matrix if needed */
    Mat nA = matis->A;

    PetscCall(MatGetLocalToGlobalMapping(nA, &lrmap, &lcmap));
    if (!lrmap && !lcmap) {
      PetscCall(MatISSetLocalMat(A, lA));
    } else {
      Mat            P = NULL, R = NULL;
      MatProductType ptype;

      if (lrmap == lcmap) {
        ptype = MATPRODUCT_PtAP;
        PetscCall(MatCreateFromISLocalToGlobalMapping(lcmap, nA, PETSC_TRUE, PETSC_FALSE, NULL, &P));
        PetscCall(MatProductCreate(lA, P, NULL, &nA));
      } else {
        if (lcmap) PetscCall(MatCreateFromISLocalToGlobalMapping(lcmap, nA, PETSC_TRUE, PETSC_FALSE, NULL, &P));
        if (lrmap) PetscCall(MatCreateFromISLocalToGlobalMapping(lrmap, nA, PETSC_FALSE, PETSC_TRUE, NULL, &R));
        if (R && P) {
          ptype = MATPRODUCT_ABC;
          PetscCall(MatProductCreate(R, lA, P, &nA));
        } else if (R) {
          ptype = MATPRODUCT_AB;
          PetscCall(MatProductCreate(R, lA, NULL, &nA));
        } else {
          ptype = MATPRODUCT_AB;
          PetscCall(MatProductCreate(lA, P, NULL, &nA));
        }
      }
      PetscCall(MatProductSetType(nA, ptype));
      PetscCall(MatProductSetFromOptions(nA));
      PetscCall(MatProductSymbolic(nA));
      PetscCall(MatProductNumeric(nA));
      PetscCall(MatProductClear(nA));
      PetscCall(MatConvert(nA, matis->lmattype, MAT_INPLACE_MATRIX, &nA));
      PetscCall(MatISSetLocalMat(A, nA));
      PetscCall(MatDestroy(&nA));
      PetscCall(MatDestroy(&P));
      PetscCall(MatDestroy(&R));
    }
  }
  PetscCall(MatDestroy(&lA));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISStoreL2L - Store local-to-local operators during the Galerkin process of computing `MatPtAP()`

  Logically Collective

  Input Parameters:
+ A     - the matrix
- store - the boolean flag

  Level: advanced

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateIS()`, `MatISSetPreallocation()`, `MatPtAP()`
@*/
PetscErrorCode MatISStoreL2L(Mat A, PetscBool store)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscValidLogicalCollectiveBool(A, store, 2);
  PetscTryMethod(A, "MatISStoreL2L_C", (Mat, PetscBool), (A, store));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISStoreL2L_IS(Mat A, PetscBool store)
{
  Mat_IS *matis = (Mat_IS *)A->data;

  PetscFunctionBegin;
  matis->storel2l = store;
  if (!store) PetscCall(PetscObjectCompose((PetscObject)A, "_MatIS_PtAP_l2l", NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISFixLocalEmpty - Compress out zero local rows from the local matrices

  Logically Collective

  Input Parameters:
+ A   - the matrix
- fix - the boolean flag

  Level: advanced

  Note:
  When `fix` is `PETSC_TRUE`, new local matrices and l2g maps are generated during the final assembly process.

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatCreate()`, `MatCreateIS()`, `MatISSetPreallocation()`, `MatAssemblyEnd()`, `MAT_FINAL_ASSEMBLY`
@*/
PetscErrorCode MatISFixLocalEmpty(Mat A, PetscBool fix)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  PetscValidLogicalCollectiveBool(A, fix, 2);
  PetscTryMethod(A, "MatISFixLocalEmpty_C", (Mat, PetscBool), (A, fix));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISFixLocalEmpty_IS(Mat A, PetscBool fix)
{
  Mat_IS *matis = (Mat_IS *)A->data;

  PetscFunctionBegin;
  matis->locempty = fix;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISSetPreallocation - Preallocates memory for a `MATIS` parallel matrix.

  Collective

  Input Parameters:
+ B     - the matrix
. d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
           (same value is used for all local rows)
. d_nnz - array containing the number of nonzeros in the various rows of the
           DIAGONAL portion of the local submatrix (possibly different for each row)
           or `NULL`, if `d_nz` is used to specify the nonzero structure.
           The size of this array is equal to the number of local rows, i.e `m`.
           For matrices that will be factored, you must leave room for (and set)
           the diagonal entry even if it is zero.
. o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
           submatrix (same value is used for all local rows).
- o_nnz - array containing the number of nonzeros in the various rows of the
           OFF-DIAGONAL portion of the local submatrix (possibly different for
           each row) or `NULL`, if `o_nz` is used to specify the nonzero
           structure. The size of this array is equal to the number
           of local rows, i.e `m`.

   If the *_nnz parameter is given then the *_nz parameter is ignored

  Level: intermediate

  Note:
  This function has the same interface as the `MATMPIAIJ` preallocation routine in order to simplify the transition
  from the asssembled format to the unassembled one. It overestimates the preallocation of `MATIS` local
  matrices; for exact preallocation, the user should set the preallocation directly on local matrix objects.

.seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateIS()`, `MatMPIAIJSetPreallocation()`, `MatISGetLocalMat()`, `MATIS`
@*/
PetscErrorCode MatISSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
  PetscValidType(B, 1);
  PetscTryMethod(B, "MatISSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetPreallocation_IS(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
{
  Mat_IS  *matis = (Mat_IS *)B->data;
  PetscInt bs, i, nlocalcols;

  PetscFunctionBegin;
  PetscCall(MatSetUp(B));
  if (!d_nnz)
    for (i = 0; i < matis->sf->nroots; i++) matis->sf_rootdata[i] = d_nz;
  else
    for (i = 0; i < matis->sf->nroots; i++) matis->sf_rootdata[i] = d_nnz[i];

  if (!o_nnz)
    for (i = 0; i < matis->sf->nroots; i++) matis->sf_rootdata[i] += o_nz;
  else
    for (i = 0; i < matis->sf->nroots; i++) matis->sf_rootdata[i] += o_nnz[i];

  PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
  PetscCall(MatGetSize(matis->A, NULL, &nlocalcols));
  PetscCall(MatGetBlockSize(matis->A, &bs));
  PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));

  for (i = 0; i < matis->sf->nleaves; i++) matis->sf_leafdata[i] = PetscMin(matis->sf_leafdata[i], nlocalcols);
  PetscCall(MatSeqAIJSetPreallocation(matis->A, 0, matis->sf_leafdata));
#if defined(PETSC_HAVE_HYPRE)
  PetscCall(MatHYPRESetPreallocation(matis->A, 0, matis->sf_leafdata, 0, NULL));
#endif

  for (i = 0; i < matis->sf->nleaves / bs; i++) {
    PetscInt b;

    matis->sf_leafdata[i] = matis->sf_leafdata[i * bs] / bs;
    for (b = 1; b < bs; b++) matis->sf_leafdata[i] = PetscMax(matis->sf_leafdata[i], matis->sf_leafdata[i * bs + b] / bs);
  }
  PetscCall(MatSeqBAIJSetPreallocation(matis->A, bs, 0, matis->sf_leafdata));

  nlocalcols /= bs;
  for (i = 0; i < matis->sf->nleaves / bs; i++) matis->sf_leafdata[i] = PetscMin(matis->sf_leafdata[i], nlocalcols - i);
  PetscCall(MatSeqSBAIJSetPreallocation(matis->A, bs, 0, matis->sf_leafdata));

  /* for other matrix types */
  PetscCall(MatSetUp(matis->A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode MatConvert_IS_XAIJ(Mat mat, MatType mtype, MatReuse reuse, Mat *M)
{
  Mat_IS            *matis     = (Mat_IS *)mat->data;
  Mat                local_mat = NULL, MT;
  PetscInt           rbs, cbs, rows, cols, lrows, lcols;
  PetscInt           local_rows, local_cols;
  PetscBool          isseqdense, isseqsbaij, isseqaij, isseqbaij;
  PetscMPIInt        size;
  const PetscScalar *array;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
  if (size == 1 && mat->rmap->N == matis->A->rmap->N && mat->cmap->N == matis->A->cmap->N && !matis->allow_repeated) {
    Mat      B;
    IS       irows = NULL, icols = NULL;
    PetscInt rbs, cbs;

    PetscCall(ISLocalToGlobalMappingGetBlockSize(matis->rmapping, &rbs));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(matis->cmapping, &cbs));
    if (reuse != MAT_REUSE_MATRIX) { /* check if l2g maps are one-to-one */
      IS              rows, cols;
      const PetscInt *ridxs, *cidxs;
      PetscInt        i, nw;
      PetscBT         work;

      PetscCall(ISLocalToGlobalMappingGetBlockIndices(matis->rmapping, &ridxs));
      PetscCall(ISLocalToGlobalMappingGetSize(matis->rmapping, &nw));
      nw = nw / rbs;
      PetscCall(PetscBTCreate(nw, &work));
      for (i = 0; i < nw; i++) PetscCall(PetscBTSet(work, ridxs[i]));
      for (i = 0; i < nw; i++)
        if (!PetscBTLookup(work, i)) break;
      if (i == nw) {
        PetscCall(ISCreateBlock(PETSC_COMM_SELF, rbs, nw, ridxs, PETSC_USE_POINTER, &rows));
        PetscCall(ISSetPermutation(rows));
        PetscCall(ISInvertPermutation(rows, PETSC_DECIDE, &irows));
        PetscCall(ISDestroy(&rows));
      }
      PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(matis->rmapping, &ridxs));
      PetscCall(PetscBTDestroy(&work));
      if (irows && matis->rmapping != matis->cmapping) {
        PetscCall(ISLocalToGlobalMappingGetBlockIndices(matis->cmapping, &cidxs));
        PetscCall(ISLocalToGlobalMappingGetSize(matis->cmapping, &nw));
        nw = nw / cbs;
        PetscCall(PetscBTCreate(nw, &work));
        for (i = 0; i < nw; i++) PetscCall(PetscBTSet(work, cidxs[i]));
        for (i = 0; i < nw; i++)
          if (!PetscBTLookup(work, i)) break;
        if (i == nw) {
          PetscCall(ISCreateBlock(PETSC_COMM_SELF, cbs, nw, cidxs, PETSC_USE_POINTER, &cols));
          PetscCall(ISSetPermutation(cols));
          PetscCall(ISInvertPermutation(cols, PETSC_DECIDE, &icols));
          PetscCall(ISDestroy(&cols));
        }
        PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(matis->cmapping, &cidxs));
        PetscCall(PetscBTDestroy(&work));
      } else if (irows) {
        PetscCall(PetscObjectReference((PetscObject)irows));
        icols = irows;
      }
    } else {
      PetscCall(PetscObjectQuery((PetscObject)*M, "_MatIS_IS_XAIJ_irows", (PetscObject *)&irows));
      PetscCall(PetscObjectQuery((PetscObject)*M, "_MatIS_IS_XAIJ_icols", (PetscObject *)&icols));
      if (irows) PetscCall(PetscObjectReference((PetscObject)irows));
      if (icols) PetscCall(PetscObjectReference((PetscObject)icols));
    }
    if (!irows || !icols) {
      PetscCall(ISDestroy(&icols));
      PetscCall(ISDestroy(&irows));
      goto general_assembly;
    }
    PetscCall(MatConvert(matis->A, mtype, MAT_INITIAL_MATRIX, &B));
    if (reuse != MAT_INPLACE_MATRIX) {
      PetscCall(MatCreateSubMatrix(B, irows, icols, reuse, M));
      PetscCall(PetscObjectCompose((PetscObject)*M, "_MatIS_IS_XAIJ_irows", (PetscObject)irows));
      PetscCall(PetscObjectCompose((PetscObject)*M, "_MatIS_IS_XAIJ_icols", (PetscObject)icols));
    } else {
      Mat C;

      PetscCall(MatCreateSubMatrix(B, irows, icols, MAT_INITIAL_MATRIX, &C));
      PetscCall(MatHeaderReplace(mat, &C));
    }
    PetscCall(MatDestroy(&B));
    PetscCall(ISDestroy(&icols));
    PetscCall(ISDestroy(&irows));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
general_assembly:
  PetscCall(MatGetSize(mat, &rows, &cols));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(matis->rmapping, &rbs));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(matis->cmapping, &cbs));
  PetscCall(MatGetLocalSize(mat, &lrows, &lcols));
  PetscCall(MatGetSize(matis->A, &local_rows, &local_cols));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)matis->A, MATSEQDENSE, &isseqdense));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)matis->A, MATSEQAIJ, &isseqaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)matis->A, MATSEQBAIJ, &isseqbaij));
  PetscCall(PetscObjectBaseTypeCompare((PetscObject)matis->A, MATSEQSBAIJ, &isseqsbaij));
  PetscCheck(isseqdense || isseqaij || isseqbaij || isseqsbaij, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for matrix type %s", ((PetscObject)matis->A)->type_name);
  if (PetscDefined(USE_DEBUG)) {
    PetscBool lb[4], bb[4];

    lb[0] = isseqdense;
    lb[1] = isseqaij;
    lb[2] = isseqbaij;
    lb[3] = isseqsbaij;
    PetscCallMPI(MPIU_Allreduce(lb, bb, 4, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    PetscCheck(bb[0] || bb[1] || bb[2] || bb[3], PETSC_COMM_SELF, PETSC_ERR_SUP, "Local matrices must have the same type");
  }

  if (reuse != MAT_REUSE_MATRIX) {
    PetscCount ncoo;
    PetscInt  *coo_i, *coo_j;

    PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &MT));
    PetscCall(MatSetSizes(MT, lrows, lcols, rows, cols));
    PetscCall(MatSetType(MT, mtype));
    PetscCall(MatSetBlockSizes(MT, rbs, cbs));
    if (!isseqaij && !isseqdense) {
      PetscCall(MatConvert(matis->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &local_mat));
    } else {
      PetscCall(PetscObjectReference((PetscObject)matis->A));
      local_mat = matis->A;
    }
    PetscCall(MatSetLocalToGlobalMapping(MT, matis->rmapping, matis->cmapping));
    if (isseqdense) {
      PetscInt nr, nc;

      PetscCall(MatGetSize(local_mat, &nr, &nc));
      ncoo = nr * nc;
      PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));
      for (PetscInt j = 0; j < nc; j++) {
        for (PetscInt i = 0; i < nr; i++) {
          coo_i[j * nr + i] = i;
          coo_j[j * nr + i] = j;
        }
      }
    } else {
      const PetscInt *ii, *jj;
      PetscInt        nr;
      PetscBool       done;

      PetscCall(MatGetRowIJ(local_mat, 0, PETSC_FALSE, PETSC_FALSE, &nr, &ii, &jj, &done));
      PetscCheck(done, PetscObjectComm((PetscObject)local_mat), PETSC_ERR_PLIB, "Error in MatGetRowIJ");
      ncoo = ii[nr];
      PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));
      PetscCall(PetscArraycpy(coo_j, jj, ncoo));
      for (PetscInt i = 0; i < nr; i++) {
        for (PetscInt j = ii[i]; j < ii[i + 1]; j++) coo_i[j] = i;
      }
      PetscCall(MatRestoreRowIJ(local_mat, 0, PETSC_FALSE, PETSC_FALSE, &nr, &ii, &jj, &done));
      PetscCheck(done, PetscObjectComm((PetscObject)local_mat), PETSC_ERR_PLIB, "Error in MatRestoreRowIJ");
    }
    PetscCall(MatSetPreallocationCOOLocal(MT, ncoo, coo_i, coo_j));
    PetscCall(PetscFree2(coo_i, coo_j));
  } else {
    PetscInt mrbs, mcbs, mrows, mcols, mlrows, mlcols;

    /* some checks */
    MT = *M;
    PetscCall(MatGetBlockSizes(MT, &mrbs, &mcbs));
    PetscCall(MatGetSize(MT, &mrows, &mcols));
    PetscCall(MatGetLocalSize(MT, &mlrows, &mlcols));
    PetscCheck(mrows == rows, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong number of rows (%" PetscInt_FMT " != %" PetscInt_FMT ")", rows, mrows);
    PetscCheck(mcols == cols, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong number of cols (%" PetscInt_FMT " != %" PetscInt_FMT ")", cols, mcols);
    PetscCheck(mlrows == lrows, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong number of local rows (%" PetscInt_FMT " != %" PetscInt_FMT ")", lrows, mlrows);
    PetscCheck(mlcols == lcols, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong number of local cols (%" PetscInt_FMT " != %" PetscInt_FMT ")", lcols, mlcols);
    PetscCheck(mrbs == rbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong row block size (%" PetscInt_FMT " != %" PetscInt_FMT ")", rbs, mrbs);
    PetscCheck(mcbs == cbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Cannot reuse matrix. Wrong col block size (%" PetscInt_FMT " != %" PetscInt_FMT ")", cbs, mcbs);
    PetscCall(MatZeroEntries(MT));
    if (!isseqaij && !isseqdense) {
      PetscCall(MatConvert(matis->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &local_mat));
    } else {
      PetscCall(PetscObjectReference((PetscObject)matis->A));
      local_mat = matis->A;
    }
  }

  /* Set values */
  if (isseqdense) {
    PetscCall(MatDenseGetArrayRead(local_mat, &array));
    PetscCall(MatSetValuesCOO(MT, array, INSERT_VALUES));
    PetscCall(MatDenseRestoreArrayRead(local_mat, &array));
  } else {
    PetscCall(MatSeqAIJGetArrayRead(local_mat, &array));
    PetscCall(MatSetValuesCOO(MT, array, INSERT_VALUES));
    PetscCall(MatSeqAIJRestoreArrayRead(local_mat, &array));
  }
  PetscCall(MatDestroy(&local_mat));
  PetscCall(MatAssemblyBegin(MT, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(MT, MAT_FINAL_ASSEMBLY));
  if (reuse == MAT_INPLACE_MATRIX) {
    PetscCall(MatHeaderReplace(mat, &MT));
  } else if (reuse == MAT_INITIAL_MATRIX) {
    *M = MT;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDuplicate_IS(Mat mat, MatDuplicateOption op, Mat *newmat)
{
  Mat_IS  *matis = (Mat_IS *)mat->data;
  PetscInt rbs, cbs, m, n, M, N;
  Mat      B, localmat;

  PetscFunctionBegin;
  PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->rmap->mapping, &rbs));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->cmap->mapping, &cbs));
  PetscCall(MatGetSize(mat, &M, &N));
  PetscCall(MatGetLocalSize(mat, &m, &n));
  PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &B));
  PetscCall(MatSetSizes(B, m, n, M, N));
  PetscCall(MatSetBlockSize(B, rbs == cbs ? rbs : 1));
  PetscCall(MatSetType(B, MATIS));
  PetscCall(MatISSetLocalMatType(B, matis->lmattype));
  PetscCall(MatISSetAllowRepeated(B, matis->allow_repeated));
  PetscCall(MatSetLocalToGlobalMapping(B, mat->rmap->mapping, mat->cmap->mapping));
  PetscCall(MatDuplicate(matis->A, op, &localmat));
  PetscCall(MatSetLocalToGlobalMapping(localmat, matis->A->rmap->mapping, matis->A->cmap->mapping));
  PetscCall(MatISSetLocalMat(B, localmat));
  PetscCall(MatDestroy(&localmat));
  PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
  *newmat = B;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatIsHermitian_IS(Mat A, PetscReal tol, PetscBool *flg)
{
  Mat_IS   *matis = (Mat_IS *)A->data;
  PetscBool local_sym;

  PetscFunctionBegin;
  PetscCall(MatIsHermitian(matis->A, tol, &local_sym));
  PetscCallMPI(MPIU_Allreduce(&local_sym, flg, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatIsSymmetric_IS(Mat A, PetscReal tol, PetscBool *flg)
{
  Mat_IS   *matis = (Mat_IS *)A->data;
  PetscBool local_sym;

  PetscFunctionBegin;
  if (matis->rmapping != matis->cmapping) {
    *flg = PETSC_FALSE;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(MatIsSymmetric(matis->A, tol, &local_sym));
  PetscCallMPI(MPIU_Allreduce(&local_sym, flg, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatIsStructurallySymmetric_IS(Mat A, PetscBool *flg)
{
  Mat_IS   *matis = (Mat_IS *)A->data;
  PetscBool local_sym;

  PetscFunctionBegin;
  if (matis->rmapping != matis->cmapping) {
    *flg = PETSC_FALSE;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(MatIsStructurallySymmetric(matis->A, &local_sym));
  PetscCallMPI(MPIU_Allreduce(&local_sym, flg, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDestroy_IS(Mat A)
{
  Mat_IS *b = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(PetscFree(b->bdiag));
  PetscCall(PetscFree(b->lmattype));
  PetscCall(MatDestroy(&b->A));
  PetscCall(VecScatterDestroy(&b->cctx));
  PetscCall(VecScatterDestroy(&b->rctx));
  PetscCall(VecDestroy(&b->x));
  PetscCall(VecDestroy(&b->y));
  PetscCall(VecDestroy(&b->counter));
  PetscCall(ISDestroy(&b->getsub_ris));
  PetscCall(ISDestroy(&b->getsub_cis));
  if (b->sf != b->csf) {
    PetscCall(PetscSFDestroy(&b->csf));
    PetscCall(PetscFree2(b->csf_rootdata, b->csf_leafdata));
  } else b->csf = NULL;
  PetscCall(PetscSFDestroy(&b->sf));
  PetscCall(PetscFree2(b->sf_rootdata, b->sf_leafdata));
  PetscCall(ISLocalToGlobalMappingDestroy(&b->rmapping));
  PetscCall(ISLocalToGlobalMappingDestroy(&b->cmapping));
  PetscCall(MatDestroy(&b->dA));
  PetscCall(MatDestroy(&b->assembledA));
  PetscCall(PetscFree(A->data));
  PetscCall(PetscObjectChangeTypeName((PetscObject)A, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetLocalMatType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISGetLocalMat_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetLocalMat_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISRestoreLocalMat_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetPreallocation_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISStoreL2L_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISFixLocalEmpty_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISGetLocalToGlobalMapping_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpiaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpibaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpisbaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqbaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqsbaij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_aij_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOOLocal_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetAllowRepeated_C", NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMult_IS(Mat A, Vec x, Vec y)
{
  Mat_IS     *is   = (Mat_IS *)A->data;
  PetscScalar zero = 0.0;

  PetscFunctionBegin;
  /*  scatter the global vector x into the local work vector */
  PetscCall(VecScatterBegin(is->cctx, x, is->x, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(is->cctx, x, is->x, INSERT_VALUES, SCATTER_FORWARD));

  /* multiply the local matrix */
  PetscCall(MatMult(is->A, is->x, is->y));

  /* scatter product back into global memory */
  PetscCall(VecSet(y, zero));
  PetscCall(VecScatterBegin(is->rctx, is->y, y, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(is->rctx, is->y, y, ADD_VALUES, SCATTER_REVERSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultAdd_IS(Mat A, Vec v1, Vec v2, Vec v3)
{
  Vec temp_vec;

  PetscFunctionBegin; /*  v3 = v2 + A * v1.*/
  if (v3 != v2) {
    PetscCall(MatMult(A, v1, v3));
    PetscCall(VecAXPY(v3, 1.0, v2));
  } else {
    PetscCall(VecDuplicate(v2, &temp_vec));
    PetscCall(MatMult(A, v1, temp_vec));
    PetscCall(VecAXPY(temp_vec, 1.0, v2));
    PetscCall(VecCopy(temp_vec, v3));
    PetscCall(VecDestroy(&temp_vec));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTranspose_IS(Mat A, Vec y, Vec x)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  /*  scatter the global vector x into the local work vector */
  PetscCall(VecScatterBegin(is->rctx, y, is->y, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(is->rctx, y, is->y, INSERT_VALUES, SCATTER_FORWARD));

  /* multiply the local matrix */
  PetscCall(MatMultTranspose(is->A, is->y, is->x));

  /* scatter product back into global vector */
  PetscCall(VecSet(x, 0));
  PetscCall(VecScatterBegin(is->cctx, is->x, x, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(is->cctx, is->x, x, ADD_VALUES, SCATTER_REVERSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTransposeAdd_IS(Mat A, Vec v1, Vec v2, Vec v3)
{
  Vec temp_vec;

  PetscFunctionBegin; /*  v3 = v2 + A' * v1.*/
  if (v3 != v2) {
    PetscCall(MatMultTranspose(A, v1, v3));
    PetscCall(VecAXPY(v3, 1.0, v2));
  } else {
    PetscCall(VecDuplicate(v2, &temp_vec));
    PetscCall(MatMultTranspose(A, v1, temp_vec));
    PetscCall(VecAXPY(temp_vec, 1.0, v2));
    PetscCall(VecCopy(temp_vec, v3));
    PetscCall(VecDestroy(&temp_vec));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode ISLocalToGlobalMappingView_Multi(ISLocalToGlobalMapping mapping, PetscInt lsize, PetscInt gsize, const PetscInt vblocks[], PetscViewer viewer)
{
  PetscInt        tr[3], n;
  const PetscInt *indices;

  PetscFunctionBegin;
  tr[0] = IS_LTOGM_FILE_CLASSID;
  tr[1] = 1;
  tr[2] = gsize;
  PetscCall(PetscViewerBinaryWrite(viewer, tr, 3, PETSC_INT));
  PetscCall(PetscViewerBinaryWriteAll(viewer, vblocks, lsize, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
  PetscCall(ISLocalToGlobalMappingGetSize(mapping, &n));
  PetscCall(ISLocalToGlobalMappingGetIndices(mapping, &indices));
  PetscCall(PetscViewerBinaryWriteAll(viewer, indices, n, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
  PetscCall(ISLocalToGlobalMappingRestoreIndices(mapping, &indices));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatView_IS(Mat A, PetscViewer viewer)
{
  Mat_IS                *a = (Mat_IS *)A->data;
  PetscViewer            sviewer;
  PetscBool              isascii, isbinary, viewl2g = PETSC_FALSE, native;
  PetscViewerFormat      format;
  ISLocalToGlobalMapping rmap, cmap;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCall(PetscViewerGetFormat(viewer, &format));
  native = (PetscBool)(format == PETSC_VIEWER_NATIVE);
  if (native) {
    rmap = A->rmap->mapping;
    cmap = A->cmap->mapping;
  } else {
    rmap = a->rmapping;
    cmap = a->cmapping;
  }
  if (isascii) {
    if (format == PETSC_VIEWER_ASCII_INFO) PetscFunctionReturn(PETSC_SUCCESS);
    if (format == PETSC_VIEWER_ASCII_INFO_DETAIL || format == PETSC_VIEWER_ASCII_MATLAB) viewl2g = PETSC_TRUE;
  } else if (isbinary) {
    PetscInt        tr[6], nr, nc, lsize = 0;
    char            lmattype[64] = {'\0'};
    PetscMPIInt     size;
    PetscBool       skipHeader, vbs = PETSC_FALSE;
    IS              is;
    const PetscInt *vblocks = NULL;

    PetscCall(PetscViewerSetUp(viewer));
    PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)A)->prefix, "-mat_is_view_variableblocksizes", &vbs, NULL));
    if (vbs) {
      PetscCall(MatGetVariableBlockSizes(a->A, &lsize, &vblocks));
      PetscCall(PetscMPIIntCast(lsize, &size));
      PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &size, 1, MPI_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
    } else {
      PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)viewer), &size));
    }
    tr[0] = MAT_FILE_CLASSID;
    tr[1] = A->rmap->N;
    tr[2] = A->cmap->N;
    tr[3] = -size; /* AIJ stores nnz here */
    tr[4] = (PetscInt)(rmap == cmap);
    tr[5] = a->allow_repeated;
    PetscCall(PetscSNPrintf(lmattype, sizeof(lmattype), "%s", a->lmattype));

    PetscCall(PetscViewerBinaryWrite(viewer, tr, PETSC_STATIC_ARRAY_LENGTH(tr), PETSC_INT));
    PetscCall(PetscViewerBinaryWrite(viewer, lmattype, sizeof(lmattype), PETSC_CHAR));

    /* first dump l2g info (we need the header for proper loading on different number of processes) */
    PetscCall(PetscViewerBinaryGetSkipHeader(viewer, &skipHeader));
    PetscCall(PetscViewerBinarySetSkipHeader(viewer, PETSC_FALSE));
    if (vbs) {
      PetscCall(ISLocalToGlobalMappingView_Multi(rmap, lsize, size, vblocks, viewer));
      if (cmap != rmap) PetscCall(ISLocalToGlobalMappingView_Multi(cmap, lsize, size, vblocks, viewer));
      PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)viewer), lsize, vblocks, PETSC_USE_POINTER, &is));
      PetscCall(ISView(is, viewer));
      PetscCall(ISView(is, viewer));
      PetscCall(ISDestroy(&is));
    } else {
      PetscCall(ISLocalToGlobalMappingView(rmap, viewer));
      if (cmap != rmap) PetscCall(ISLocalToGlobalMappingView(cmap, viewer));

      /* then the sizes of the local matrices */
      PetscCall(MatGetSize(a->A, &nr, &nc));
      PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)viewer), 1, &nr, PETSC_USE_POINTER, &is));
      PetscCall(ISView(is, viewer));
      PetscCall(ISDestroy(&is));
      PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)viewer), 1, &nc, PETSC_USE_POINTER, &is));
      PetscCall(ISView(is, viewer));
      PetscCall(ISDestroy(&is));
    }
    PetscCall(PetscViewerBinarySetSkipHeader(viewer, skipHeader));
  }
  if (format == PETSC_VIEWER_ASCII_MATLAB) {
    char        name[64];
    PetscMPIInt size, rank;

    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)viewer), &size));
    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)viewer), &rank));
    if (size > 1) PetscCall(PetscSNPrintf(name, sizeof(name), "lmat_%d", rank));
    else PetscCall(PetscSNPrintf(name, sizeof(name), "lmat"));
    PetscCall(PetscObjectSetName((PetscObject)a->A, name));
  }

  /* Dump the local matrices */
  if (isbinary) { /* ViewerGetSubViewer does not work in parallel */
    PetscBool   isaij;
    PetscInt    nr, nc;
    Mat         lA, B;
    Mat_MPIAIJ *b;

    /* We create a temporary MPIAIJ matrix that stores the unassembled operator */
    PetscCall(PetscObjectBaseTypeCompare((PetscObject)a->A, MATAIJ, &isaij));
    if (!isaij) PetscCall(MatConvert(a->A, MATSEQAIJ, MAT_INITIAL_MATRIX, &lA));
    else {
      PetscCall(PetscObjectReference((PetscObject)a->A));
      lA = a->A;
    }
    PetscCall(MatCreate(PetscObjectComm((PetscObject)viewer), &B));
    PetscCall(MatSetType(B, MATMPIAIJ));
    PetscCall(MatGetSize(lA, &nr, &nc));
    PetscCall(MatSetSizes(B, nr, nc, PETSC_DECIDE, PETSC_DECIDE));
    PetscCall(MatMPIAIJSetPreallocation(B, 0, NULL, 0, NULL));

    b = (Mat_MPIAIJ *)B->data;
    PetscCall(MatDestroy(&b->A));
    b->A = lA;

    PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    PetscCall(MatView(B, viewer));
    PetscCall(MatDestroy(&B));
  } else {
    PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    PetscCall(MatView(a->A, sviewer));
    PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
  }

  /* with ASCII, we dump the l2gmaps at the end */
  if (viewl2g) {
    if (format == PETSC_VIEWER_ASCII_MATLAB) {
      PetscCall(PetscObjectSetName((PetscObject)rmap, "row"));
      PetscCall(ISLocalToGlobalMappingView(rmap, viewer));
      PetscCall(PetscObjectSetName((PetscObject)cmap, "col"));
      PetscCall(ISLocalToGlobalMappingView(cmap, viewer));
    } else {
      PetscCall(ISLocalToGlobalMappingView(rmap, viewer));
      PetscCall(ISLocalToGlobalMappingView(cmap, viewer));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode ISLocalToGlobalMappingHasRepeatedLocal_Private(ISLocalToGlobalMapping map, PetscBool *has)
{
  const PetscInt *idxs;
  PetscHSetI      ht;
  PetscInt        n, bs;

  PetscFunctionBegin;
  PetscCall(ISLocalToGlobalMappingGetSize(map, &n));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(map, &bs));
  PetscCall(ISLocalToGlobalMappingGetBlockIndices(map, &idxs));
  PetscCall(PetscHSetICreate(&ht));
  *has = PETSC_FALSE;
  for (PetscInt i = 0; i < n / bs; i++) {
    PetscBool missing = PETSC_TRUE;
    if (idxs[i] < 0) continue;
    PetscCall(PetscHSetIQueryAdd(ht, idxs[i], &missing));
    if (!missing) {
      *has = PETSC_TRUE;
      break;
    }
  }
  PetscCall(PetscHSetIDestroy(&ht));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatLoad_IS(Mat A, PetscViewer viewer)
{
  ISLocalToGlobalMapping rmap, cmap;
  MPI_Comm               comm = PetscObjectComm((PetscObject)A);
  PetscBool              isbinary, samel, allow, isbaij;
  PetscInt               tr[6], M, N, nr, nc, Asize, isn;
  const PetscInt        *idx;
  PetscMPIInt            size;
  char                   lmattype[64];
  Mat                    dA, lA;
  IS                     is;

  PetscFunctionBegin;
  PetscCheckSameComm(A, 1, viewer, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
  PetscCheck(isbinary, PetscObjectComm((PetscObject)viewer), PETSC_ERR_SUP, "Invalid viewer of type %s", ((PetscObject)viewer)->type_name);

  PetscCall(PetscViewerBinaryRead(viewer, tr, PETSC_STATIC_ARRAY_LENGTH(tr), NULL, PETSC_INT));
  PetscCheck(tr[0] == MAT_FILE_CLASSID, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a matrix next in file");
  PetscCheck(tr[1] >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a IS matrix next in file");
  PetscCheck(tr[2] >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a IS matrix next in file");
  PetscCheck(tr[3] < 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a IS matrix next in file");
  PetscCheck(tr[4] == 0 || tr[4] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a IS matrix next in file");
  PetscCheck(tr[5] == 0 || tr[5] == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Not a IS matrix next in file");
  M     = tr[1];
  N     = tr[2];
  Asize = -tr[3];
  samel = (PetscBool)tr[4];
  allow = (PetscBool)tr[5];
  PetscCall(PetscViewerBinaryRead(viewer, lmattype, sizeof(lmattype), NULL, PETSC_CHAR));

  /* if we are loading from a larger set of processes, allow repeated entries */
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)viewer), &size));
  if (Asize > size) allow = PETSC_TRUE;

  /* set global sizes if not set already */
  if (A->rmap->N < 0) A->rmap->N = M;
  if (A->cmap->N < 0) A->cmap->N = N;
  PetscCall(PetscLayoutSetUp(A->rmap));
  PetscCall(PetscLayoutSetUp(A->cmap));
  PetscCheck(M == A->rmap->N, comm, PETSC_ERR_ARG_SIZ, "Matrix rows should be %" PetscInt_FMT ", found %" PetscInt_FMT, M, A->rmap->N);
  PetscCheck(N == A->cmap->N, comm, PETSC_ERR_ARG_SIZ, "Matrix columns should be %" PetscInt_FMT ", found %" PetscInt_FMT, N, A->cmap->N);

  /* load l2g maps */
  PetscCall(ISLocalToGlobalMappingCreate(comm, 0, 0, NULL, PETSC_USE_POINTER, &rmap));
  PetscCall(ISLocalToGlobalMappingLoad(rmap, viewer));
  if (!samel) {
    PetscCall(ISLocalToGlobalMappingCreate(comm, 0, 0, NULL, PETSC_USE_POINTER, &cmap));
    PetscCall(ISLocalToGlobalMappingLoad(cmap, viewer));
  } else {
    PetscCall(PetscObjectReference((PetscObject)rmap));
    cmap = rmap;
  }

  /* load sizes of local matrices */
  PetscCall(ISCreate(comm, &is));
  PetscCall(ISSetType(is, ISGENERAL));
  PetscCall(ISLoad(is, viewer));
  PetscCall(ISGetLocalSize(is, &isn));
  PetscCall(ISGetIndices(is, &idx));
  nr = 0;
  for (PetscInt i = 0; i < isn; i++) nr += idx[i];
  PetscCall(ISRestoreIndices(is, &idx));
  PetscCall(ISDestroy(&is));
  PetscCall(ISCreate(comm, &is));
  PetscCall(ISSetType(is, ISGENERAL));
  PetscCall(ISLoad(is, viewer));
  PetscCall(ISGetLocalSize(is, &isn));
  PetscCall(ISGetIndices(is, &idx));
  nc = 0;
  for (PetscInt i = 0; i < isn; i++) nc += idx[i];
  PetscCall(ISRestoreIndices(is, &idx));
  PetscCall(ISDestroy(&is));

  /* now load the unassembled operator */
  PetscCall(MatCreate(comm, &dA));
  PetscCall(MatSetType(dA, MATMPIAIJ));
  PetscCall(MatSetSizes(dA, nr, nc, PETSC_DECIDE, PETSC_DECIDE));
  PetscCall(MatLoad(dA, viewer));
  PetscCall(MatMPIAIJGetSeqAIJ(dA, &lA, NULL, NULL));
  PetscCall(PetscObjectReference((PetscObject)lA));
  PetscCall(MatDestroy(&dA));

  /* and convert to the desired format */
  PetscCall(PetscStrcmpAny(lmattype, &isbaij, MATSBAIJ, MATSEQSBAIJ, ""));
  if (isbaij) PetscCall(MatSetOption(lA, MAT_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatConvert(lA, lmattype, MAT_INPLACE_MATRIX, &lA));

  /* check if we actually have repeated entries */
  if (allow) {
    PetscBool rhas, chas, hasrepeated;

    PetscCall(ISLocalToGlobalMappingHasRepeatedLocal_Private(rmap, &rhas));
    if (rmap != cmap) PetscCall(ISLocalToGlobalMappingHasRepeatedLocal_Private(cmap, &chas));
    else chas = rhas;
    hasrepeated = (PetscBool)(rhas || chas);
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &hasrepeated, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));
    if (!hasrepeated) allow = PETSC_FALSE;
  }

  /* assemble the MATIS object */
  PetscCall(MatISSetAllowRepeated(A, allow));
  PetscCall(MatSetLocalToGlobalMapping(A, rmap, cmap));
  PetscCall(MatISSetLocalMat(A, lA));
  PetscCall(MatDestroy(&lA));
  PetscCall(ISLocalToGlobalMappingDestroy(&rmap));
  PetscCall(ISLocalToGlobalMappingDestroy(&cmap));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatInvertBlockDiagonal_IS(Mat mat, const PetscScalar **values)
{
  Mat_IS            *is = (Mat_IS *)mat->data;
  MPI_Datatype       nodeType;
  const PetscScalar *lv;
  PetscInt           bs;
  PetscMPIInt        mbs;

  PetscFunctionBegin;
  PetscCall(MatGetBlockSize(mat, &bs));
  PetscCall(MatSetBlockSize(is->A, bs));
  PetscCall(MatInvertBlockDiagonal(is->A, &lv));
  if (!is->bdiag) PetscCall(PetscMalloc1(bs * mat->rmap->n, &is->bdiag));
  PetscCall(PetscMPIIntCast(bs, &mbs));
  PetscCallMPI(MPI_Type_contiguous(mbs, MPIU_SCALAR, &nodeType));
  PetscCallMPI(MPI_Type_commit(&nodeType));
  PetscCall(PetscSFReduceBegin(is->sf, nodeType, lv, is->bdiag, MPI_REPLACE));
  PetscCall(PetscSFReduceEnd(is->sf, nodeType, lv, is->bdiag, MPI_REPLACE));
  PetscCallMPI(MPI_Type_free(&nodeType));
  if (values) *values = is->bdiag;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetUpScatters_Private(Mat A)
{
  Vec             cglobal, rglobal;
  IS              from;
  Mat_IS         *is = (Mat_IS *)A->data;
  PetscScalar     sum;
  const PetscInt *garray;
  PetscInt        nr, rbs, nc, cbs;
  VecType         rtype;

  PetscFunctionBegin;
  PetscCall(ISLocalToGlobalMappingGetSize(is->rmapping, &nr));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(is->rmapping, &rbs));
  PetscCall(ISLocalToGlobalMappingGetSize(is->cmapping, &nc));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(is->cmapping, &cbs));
  PetscCall(VecDestroy(&is->x));
  PetscCall(VecDestroy(&is->y));
  PetscCall(VecDestroy(&is->counter));
  PetscCall(VecScatterDestroy(&is->rctx));
  PetscCall(VecScatterDestroy(&is->cctx));
  PetscCall(MatCreateVecs(is->A, &is->x, &is->y));
  PetscCall(VecBindToCPU(is->y, PETSC_TRUE));
  PetscCall(VecGetRootType_Private(is->y, &rtype));
  PetscCall(PetscFree(A->defaultvectype));
  PetscCall(PetscStrallocpy(rtype, &A->defaultvectype));
  PetscCall(MatCreateVecs(A, &cglobal, &rglobal));
  PetscCall(VecBindToCPU(rglobal, PETSC_TRUE));
  PetscCall(ISLocalToGlobalMappingGetBlockIndices(is->rmapping, &garray));
  PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)A), rbs, nr / rbs, garray, PETSC_USE_POINTER, &from));
  PetscCall(VecScatterCreate(rglobal, from, is->y, NULL, &is->rctx));
  PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(is->rmapping, &garray));
  PetscCall(ISDestroy(&from));
  if (is->rmapping != is->cmapping) {
    PetscCall(ISLocalToGlobalMappingGetBlockIndices(is->cmapping, &garray));
    PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)A), cbs, nc / cbs, garray, PETSC_USE_POINTER, &from));
    PetscCall(VecScatterCreate(cglobal, from, is->x, NULL, &is->cctx));
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(is->cmapping, &garray));
    PetscCall(ISDestroy(&from));
  } else {
    PetscCall(PetscObjectReference((PetscObject)is->rctx));
    is->cctx = is->rctx;
  }
  PetscCall(VecDestroy(&cglobal));

  /* interface counter vector (local) */
  PetscCall(VecDuplicate(is->y, &is->counter));
  PetscCall(VecBindToCPU(is->counter, PETSC_TRUE));
  PetscCall(VecSet(is->y, 1.));
  PetscCall(VecScatterBegin(is->rctx, is->y, rglobal, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(is->rctx, is->y, rglobal, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterBegin(is->rctx, rglobal, is->counter, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(is->rctx, rglobal, is->counter, INSERT_VALUES, SCATTER_FORWARD));
  PetscCall(VecBindToCPU(is->y, PETSC_FALSE));
  PetscCall(VecBindToCPU(is->counter, PETSC_FALSE));

  /* special functions for block-diagonal matrices */
  PetscCall(VecSum(rglobal, &sum));
  A->ops->invertblockdiagonal = NULL;
  if ((PetscInt)(PetscRealPart(sum)) == A->rmap->N && A->rmap->N == A->cmap->N && is->rmapping == is->cmapping) A->ops->invertblockdiagonal = MatInvertBlockDiagonal_IS;
  PetscCall(VecDestroy(&rglobal));

  /* setup SF for general purpose shared indices based communications */
  PetscCall(MatISSetUpSF_IS(A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISFilterL2GMap(Mat A, ISLocalToGlobalMapping map, ISLocalToGlobalMapping *nmap, ISLocalToGlobalMapping *lmap)
{
  Mat_IS                    *matis = (Mat_IS *)A->data;
  IS                         is;
  ISLocalToGlobalMappingType l2gtype;
  const PetscInt            *idxs;
  PetscHSetI                 ht;
  PetscInt                  *nidxs;
  PetscInt                   i, n, bs, c;
  PetscBool                  flg[] = {PETSC_FALSE, PETSC_FALSE};

  PetscFunctionBegin;
  PetscCall(ISLocalToGlobalMappingGetSize(map, &n));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(map, &bs));
  PetscCall(ISLocalToGlobalMappingGetBlockIndices(map, &idxs));
  PetscCall(PetscHSetICreate(&ht));
  PetscCall(PetscMalloc1(n / bs, &nidxs));
  for (i = 0, c = 0; i < n / bs; i++) {
    PetscBool missing = PETSC_TRUE;
    if (idxs[i] < 0) {
      flg[0] = PETSC_TRUE;
      continue;
    }
    if (!matis->allow_repeated) PetscCall(PetscHSetIQueryAdd(ht, idxs[i], &missing));
    if (!missing) flg[1] = PETSC_TRUE;
    else nidxs[c++] = idxs[i];
  }
  PetscCall(PetscHSetIDestroy(&ht));
  PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, flg, 2, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));
  if (!flg[0] && !flg[1]) { /* Entries are all non negative and unique */
    *nmap = NULL;
    *lmap = NULL;
    PetscCall(PetscFree(nidxs));
    PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(map, &idxs));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  /* New l2g map without negative indices (and repeated indices if not allowed) */
  PetscCall(ISCreateBlock(PetscObjectComm((PetscObject)A), bs, c, nidxs, PETSC_USE_POINTER, &is));
  PetscCall(ISLocalToGlobalMappingCreateIS(is, nmap));
  PetscCall(ISDestroy(&is));
  PetscCall(ISLocalToGlobalMappingGetType(map, &l2gtype));
  PetscCall(ISLocalToGlobalMappingSetType(*nmap, l2gtype));

  /* New local l2g map for repeated indices if not allowed */
  PetscCall(ISGlobalToLocalMappingApplyBlock(*nmap, IS_GTOLM_MASK, n / bs, idxs, NULL, nidxs));
  PetscCall(ISCreateBlock(PETSC_COMM_SELF, bs, n / bs, nidxs, PETSC_USE_POINTER, &is));
  PetscCall(ISLocalToGlobalMappingCreateIS(is, lmap));
  PetscCall(ISDestroy(&is));
  PetscCall(PetscFree(nidxs));
  PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(map, &idxs));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetLocalToGlobalMapping_IS(Mat A, ISLocalToGlobalMapping rmapping, ISLocalToGlobalMapping cmapping)
{
  Mat_IS                *is            = (Mat_IS *)A->data;
  ISLocalToGlobalMapping localrmapping = NULL, localcmapping = NULL;
  PetscInt               nr, rbs, nc, cbs;
  PetscBool              cong, freem[] = {PETSC_FALSE, PETSC_FALSE};

  PetscFunctionBegin;
  if (rmapping) PetscCheckSameComm(A, 1, rmapping, 2);
  if (cmapping) PetscCheckSameComm(A, 1, cmapping, 3);

  PetscCall(ISLocalToGlobalMappingDestroy(&is->rmapping));
  PetscCall(ISLocalToGlobalMappingDestroy(&is->cmapping));
  PetscCall(PetscLayoutSetUp(A->rmap));
  PetscCall(PetscLayoutSetUp(A->cmap));
  PetscCall(MatHasCongruentLayouts(A, &cong));

  /* If NULL, local space matches global space */
  if (!rmapping) {
    IS is;

    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), A->rmap->N, 0, 1, &is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &rmapping));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(rmapping, A->rmap->bs));
    PetscCall(ISDestroy(&is));
    freem[0] = PETSC_TRUE;
    if (!cmapping && cong && A->rmap->bs == A->cmap->bs) cmapping = rmapping;
  } else if (!is->islocalref) { /* check if the l2g map has negative or repeated entries */
    PetscCall(MatISFilterL2GMap(A, rmapping, &is->rmapping, &localrmapping));
    if (rmapping == cmapping) {
      PetscCall(PetscObjectReference((PetscObject)is->rmapping));
      is->cmapping = is->rmapping;
      PetscCall(PetscObjectReference((PetscObject)localrmapping));
      localcmapping = localrmapping;
    }
  }
  if (!cmapping) {
    IS is;

    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), A->cmap->N, 0, 1, &is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &cmapping));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(cmapping, A->cmap->bs));
    PetscCall(ISDestroy(&is));
    freem[1] = PETSC_TRUE;
  } else if (cmapping != rmapping && !is->islocalref) { /* check if the l2g map has negative or repeated entries */
    PetscCall(MatISFilterL2GMap(A, cmapping, &is->cmapping, &localcmapping));
  }
  if (!is->rmapping) {
    PetscCall(PetscObjectReference((PetscObject)rmapping));
    is->rmapping = rmapping;
  }
  if (!is->cmapping) {
    PetscCall(PetscObjectReference((PetscObject)cmapping));
    is->cmapping = cmapping;
  }

  /* Clean up */
  is->lnnzstate = 0;
  PetscCall(MatDestroy(&is->dA));
  PetscCall(MatDestroy(&is->assembledA));
  PetscCall(MatDestroy(&is->A));
  if (is->csf != is->sf) {
    PetscCall(PetscSFDestroy(&is->csf));
    PetscCall(PetscFree2(is->csf_rootdata, is->csf_leafdata));
  } else is->csf = NULL;
  PetscCall(PetscSFDestroy(&is->sf));
  PetscCall(PetscFree2(is->sf_rootdata, is->sf_leafdata));
  PetscCall(PetscFree(is->bdiag));

  /* check if the two mappings are actually the same for square matrices since MATIS has some optimization for this case
     (DOLFIN passes 2 different objects) */
  PetscCall(ISLocalToGlobalMappingGetSize(is->rmapping, &nr));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(is->rmapping, &rbs));
  PetscCall(ISLocalToGlobalMappingGetSize(is->cmapping, &nc));
  PetscCall(ISLocalToGlobalMappingGetBlockSize(is->cmapping, &cbs));
  if (is->rmapping != is->cmapping && cong) {
    PetscBool same = PETSC_FALSE;
    if (nr == nc && cbs == rbs) {
      const PetscInt *idxs1, *idxs2;

      PetscCall(ISLocalToGlobalMappingGetBlockIndices(is->rmapping, &idxs1));
      PetscCall(ISLocalToGlobalMappingGetBlockIndices(is->cmapping, &idxs2));
      PetscCall(PetscArraycmp(idxs1, idxs2, nr / rbs, &same));
      PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(is->rmapping, &idxs1));
      PetscCall(ISLocalToGlobalMappingRestoreBlockIndices(is->cmapping, &idxs2));
    }
    PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &same, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
    if (same) {
      PetscCall(ISLocalToGlobalMappingDestroy(&is->cmapping));
      PetscCall(PetscObjectReference((PetscObject)is->rmapping));
      is->cmapping = is->rmapping;
    }
  }
  PetscCall(PetscLayoutSetBlockSize(A->rmap, rbs));
  PetscCall(PetscLayoutSetBlockSize(A->cmap, cbs));
  /* Pass the user defined maps to the layout */
  PetscCall(PetscLayoutSetISLocalToGlobalMapping(A->rmap, rmapping));
  PetscCall(PetscLayoutSetISLocalToGlobalMapping(A->cmap, cmapping));
  if (freem[0]) PetscCall(ISLocalToGlobalMappingDestroy(&rmapping));
  if (freem[1]) PetscCall(ISLocalToGlobalMappingDestroy(&cmapping));

  if (!is->islocalref) {
    /* Create the local matrix A */
    PetscCall(MatCreate(PETSC_COMM_SELF, &is->A));
    PetscCall(MatSetType(is->A, is->lmattype));
    PetscCall(MatSetSizes(is->A, nr, nc, nr, nc));
    PetscCall(MatSetBlockSizes(is->A, rbs, cbs));
    PetscCall(MatSetOptionsPrefix(is->A, "is_"));
    PetscCall(MatAppendOptionsPrefix(is->A, ((PetscObject)A)->prefix));
    PetscCall(PetscLayoutSetUp(is->A->rmap));
    PetscCall(PetscLayoutSetUp(is->A->cmap));
    PetscCall(MatSetLocalToGlobalMapping(is->A, localrmapping, localcmapping));
    PetscCall(ISLocalToGlobalMappingDestroy(&localrmapping));
    PetscCall(ISLocalToGlobalMappingDestroy(&localcmapping));
    /* setup scatters and local vectors for MatMult */
    PetscCall(MatISSetUpScatters_Private(A));
  }
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetUp_IS(Mat A)
{
  Mat_IS                *is = (Mat_IS *)A->data;
  ISLocalToGlobalMapping rmap, cmap;

  PetscFunctionBegin;
  if (!is->sf) {
    PetscCall(MatGetLocalToGlobalMapping(A, &rmap, &cmap));
    PetscCall(MatSetLocalToGlobalMapping(A, rmap, cmap));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValues_IS(Mat mat, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  Mat_IS  *is = (Mat_IS *)mat->data;
  PetscInt buf[2 * MATIS_MAX_ENTRIES_INSERTION], *rows_l = NULL, *cols_l = NULL;

  PetscFunctionBegin;
  IndexSpaceGet(buf, m, n, rows_l, cols_l);
  PetscCall(ISGlobalToLocalMappingApply(is->rmapping, IS_GTOLM_MASK, m, rows, &m, rows_l));
  if (m != n || rows != cols || is->cmapping != is->rmapping) {
    PetscCall(ISGlobalToLocalMappingApply(is->cmapping, IS_GTOLM_MASK, n, cols, &n, cols_l));
    PetscCall(MatSetValues(is->A, m, rows_l, n, cols_l, values, addv));
  } else {
    PetscCall(MatSetValues(is->A, m, rows_l, m, rows_l, values, addv));
  }
  IndexSpaceRestore(buf, m, n, rows_l, cols_l);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesBlocked_IS(Mat mat, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  Mat_IS  *is = (Mat_IS *)mat->data;
  PetscInt buf[2 * MATIS_MAX_ENTRIES_INSERTION], *rows_l = NULL, *cols_l = NULL;

  PetscFunctionBegin;
  IndexSpaceGet(buf, m, n, rows_l, cols_l);
  PetscCall(ISGlobalToLocalMappingApplyBlock(is->rmapping, IS_GTOLM_MASK, m, rows, &m, rows_l));
  if (m != n || rows != cols || is->cmapping != is->rmapping) {
    PetscCall(ISGlobalToLocalMappingApplyBlock(is->cmapping, IS_GTOLM_MASK, n, cols, &n, cols_l));
    PetscCall(MatSetValuesBlocked(is->A, m, rows_l, n, cols_l, values, addv));
  } else {
    PetscCall(MatSetValuesBlocked(is->A, m, rows_l, m, rows_l, values, addv));
  }
  IndexSpaceRestore(buf, m, n, rows_l, cols_l);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesLocal_IS(Mat A, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  if (is->A->rmap->mapping || is->A->cmap->mapping) {
    PetscCall(MatSetValuesLocal(is->A, m, rows, n, cols, values, addv));
  } else {
    PetscCall(MatSetValues(is->A, m, rows, n, cols, values, addv));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesBlockedLocal_IS(Mat A, PetscInt m, const PetscInt *rows, PetscInt n, const PetscInt *cols, const PetscScalar *values, InsertMode addv)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  if (is->A->rmap->mapping || is->A->cmap->mapping) {
    PetscCall(MatSetValuesBlockedLocal(is->A, m, rows, n, cols, values, addv));
  } else {
    PetscCall(MatSetValuesBlocked(is->A, m, rows, n, cols, values, addv));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISZeroRowsColumnsLocal_Private(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, PetscBool columns)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  if (!n) PetscFunctionReturn(PETSC_SUCCESS);
  is->pure_neumann = PETSC_FALSE;

  if (columns) {
    PetscCall(MatZeroRowsColumns(is->A, n, rows, diag, NULL, NULL));
  } else {
    PetscCall(MatZeroRows(is->A, n, rows, diag, NULL, NULL));
  }
  if (diag != 0.) {
    const PetscScalar *array;

    PetscCall(VecGetArrayRead(is->counter, &array));
    for (PetscInt i = 0; i < n; i++) PetscCall(MatSetValue(is->A, rows[i], rows[i], diag / (array[rows[i]]), INSERT_VALUES));
    PetscCall(VecRestoreArrayRead(is->counter, &array));
    PetscCall(MatAssemblyBegin(is->A, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(is->A, MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsColumns_Private_IS(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b, PetscBool columns)
{
  Mat_IS   *matis = (Mat_IS *)A->data;
  PetscInt  nr, nl, len;
  PetscInt *lrows = NULL;

  PetscFunctionBegin;
  if (PetscUnlikelyDebug(columns || diag != 0. || (x && b))) {
    PetscBool cong;

    PetscCall(PetscLayoutCompare(A->rmap, A->cmap, &cong));
    cong = (PetscBool)(cong && matis->sf == matis->csf);
    PetscCheck(cong || !columns, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Columns can be zeroed if and only if A->rmap and A->cmap are congruent and the l2g maps are the same for MATIS");
    PetscCheck(cong || diag == 0., PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Nonzero diagonal value supported if and only if A->rmap and A->cmap are congruent and the l2g maps are the same for MATIS");
    PetscCheck(cong || !x || !b, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "A->rmap and A->cmap need to be congruent, and the l2g maps be the same");
  }
  PetscCall(MatGetSize(matis->A, &nl, NULL));
  /* get locally owned rows */
  PetscCall(PetscLayoutMapLocal(A->rmap, n, rows, &len, &lrows, NULL));
  /* fix right-hand side if needed */
  if (x && b) {
    const PetscScalar *xx;
    PetscScalar       *bb;

    PetscCall(VecGetArrayRead(x, &xx));
    PetscCall(VecGetArray(b, &bb));
    for (PetscInt i = 0; i < len; ++i) bb[lrows[i]] = diag * xx[lrows[i]];
    PetscCall(VecRestoreArrayRead(x, &xx));
    PetscCall(VecRestoreArray(b, &bb));
  }
  /* get rows associated to the local matrices */
  PetscCall(PetscArrayzero(matis->sf_leafdata, nl));
  PetscCall(PetscArrayzero(matis->sf_rootdata, A->rmap->n));
  for (PetscInt i = 0; i < len; i++) matis->sf_rootdata[lrows[i]] = 1;
  PetscCall(PetscFree(lrows));
  PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
  PetscCall(PetscMalloc1(nl, &lrows));
  nr = 0;
  for (PetscInt i = 0; i < nl; i++)
    if (matis->sf_leafdata[i]) lrows[nr++] = i;
  PetscCall(MatISZeroRowsColumnsLocal_Private(A, nr, lrows, diag, columns));
  PetscCall(PetscFree(lrows));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRows_IS(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  PetscFunctionBegin;
  PetscCall(MatZeroRowsColumns_Private_IS(A, n, rows, diag, x, b, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroRowsColumns_IS(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
{
  PetscFunctionBegin;
  PetscCall(MatZeroRowsColumns_Private_IS(A, n, rows, diag, x, b, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyBegin_IS(Mat A, MatAssemblyType type)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(MatAssemblyBegin(is->A, type));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAssemblyEnd_IS(Mat A, MatAssemblyType type)
{
  Mat_IS   *is = (Mat_IS *)A->data;
  PetscBool lnnz;

  PetscFunctionBegin;
  PetscCall(MatAssemblyEnd(is->A, type));
  /* fix for local empty rows/cols */
  if (is->locempty && type == MAT_FINAL_ASSEMBLY) {
    Mat                    newlA;
    ISLocalToGlobalMapping rl2g, cl2g;
    IS                     nzr, nzc;
    PetscInt               nr, nc, nnzr, nnzc;
    PetscBool              lnewl2g, newl2g;

    PetscCall(MatGetSize(is->A, &nr, &nc));
    PetscCall(MatFindNonzeroRowsOrCols_Basic(is->A, PETSC_FALSE, PETSC_SMALL, &nzr));
    if (!nzr) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)is->A), nr, 0, 1, &nzr));
    PetscCall(MatFindNonzeroRowsOrCols_Basic(is->A, PETSC_TRUE, PETSC_SMALL, &nzc));
    if (!nzc) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)is->A), nc, 0, 1, &nzc));
    PetscCall(ISGetSize(nzr, &nnzr));
    PetscCall(ISGetSize(nzc, &nnzc));
    if (nnzr != nr || nnzc != nc) { /* need new global l2g map */
      lnewl2g = PETSC_TRUE;
      PetscCallMPI(MPIU_Allreduce(&lnewl2g, &newl2g, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));

      /* extract valid submatrix */
      PetscCall(MatCreateSubMatrix(is->A, nzr, nzc, MAT_INITIAL_MATRIX, &newlA));
    } else { /* local matrix fully populated */
      lnewl2g = PETSC_FALSE;
      PetscCallMPI(MPIU_Allreduce(&lnewl2g, &newl2g, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));
      PetscCall(PetscObjectReference((PetscObject)is->A));
      newlA = is->A;
    }

    /* attach new global l2g map if needed */
    if (newl2g) {
      IS              zr, zc;
      const PetscInt *ridxs, *cidxs, *zridxs, *zcidxs;
      PetscInt       *nidxs, i;

      PetscCall(ISComplement(nzr, 0, nr, &zr));
      PetscCall(ISComplement(nzc, 0, nc, &zc));
      PetscCall(PetscMalloc1(PetscMax(nr, nc), &nidxs));
      PetscCall(ISLocalToGlobalMappingGetIndices(is->rmapping, &ridxs));
      PetscCall(ISLocalToGlobalMappingGetIndices(is->cmapping, &cidxs));
      PetscCall(ISGetIndices(zr, &zridxs));
      PetscCall(ISGetIndices(zc, &zcidxs));
      PetscCall(ISGetLocalSize(zr, &nnzr));
      PetscCall(ISGetLocalSize(zc, &nnzc));

      PetscCall(PetscArraycpy(nidxs, ridxs, nr));
      for (i = 0; i < nnzr; i++) nidxs[zridxs[i]] = -1;
      PetscCall(ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)A), 1, nr, nidxs, PETSC_COPY_VALUES, &rl2g));
      PetscCall(PetscArraycpy(nidxs, cidxs, nc));
      for (i = 0; i < nnzc; i++) nidxs[zcidxs[i]] = -1;
      PetscCall(ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)A), 1, nc, nidxs, PETSC_COPY_VALUES, &cl2g));

      PetscCall(ISRestoreIndices(zr, &zridxs));
      PetscCall(ISRestoreIndices(zc, &zcidxs));
      PetscCall(ISLocalToGlobalMappingRestoreIndices(is->rmapping, &ridxs));
      PetscCall(ISLocalToGlobalMappingRestoreIndices(is->cmapping, &cidxs));
      PetscCall(ISDestroy(&nzr));
      PetscCall(ISDestroy(&nzc));
      PetscCall(ISDestroy(&zr));
      PetscCall(ISDestroy(&zc));
      PetscCall(PetscFree(nidxs));
      PetscCall(MatSetLocalToGlobalMapping(A, rl2g, cl2g));
      PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
      PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));
    }
    PetscCall(MatISSetLocalMat(A, newlA));
    PetscCall(MatDestroy(&newlA));
    PetscCall(ISDestroy(&nzr));
    PetscCall(ISDestroy(&nzc));
    is->locempty = PETSC_FALSE;
  }
  lnnz          = (PetscBool)(is->A->nonzerostate == is->lnnzstate);
  is->lnnzstate = is->A->nonzerostate;
  PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &lnnz, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
  if (!lnnz) A->nonzerostate++;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISGetLocalMat_IS(Mat mat, Mat *local)
{
  Mat_IS *is = (Mat_IS *)mat->data;

  PetscFunctionBegin;
  *local = is->A;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISRestoreLocalMat_IS(Mat mat, Mat *local)
{
  PetscFunctionBegin;
  *local = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISGetLocalMat - Gets the local matrix stored inside a `MATIS` matrix.

  Not Collective.

  Input Parameter:
. mat - the matrix

  Output Parameter:
. local - the local matrix

  Level: intermediate

  Notes:
  This can be called if you have precomputed the nonzero structure of the
  matrix and want to provide it to the inner matrix object to improve the performance
  of the `MatSetValues()` operation.

  Call `MatISRestoreLocalMat()` when finished with the local matrix.

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatISRestoreLocalMat()`
@*/
PetscErrorCode MatISGetLocalMat(Mat mat, Mat *local)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscAssertPointer(local, 2);
  PetscUseMethod(mat, "MatISGetLocalMat_C", (Mat, Mat *), (mat, local));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISRestoreLocalMat - Restores the local matrix obtained with `MatISGetLocalMat()`

  Not Collective.

  Input Parameters:
+ mat   - the matrix
- local - the local matrix

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatISGetLocalMat()`
@*/
PetscErrorCode MatISRestoreLocalMat(Mat mat, Mat *local)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscAssertPointer(local, 2);
  PetscUseMethod(mat, "MatISRestoreLocalMat_C", (Mat, Mat *), (mat, local));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetLocalMatType_IS(Mat mat, MatType mtype)
{
  Mat_IS *is = (Mat_IS *)mat->data;

  PetscFunctionBegin;
  if (is->A) PetscCall(MatSetType(is->A, mtype));
  PetscCall(PetscFree(is->lmattype));
  PetscCall(PetscStrallocpy(mtype, &is->lmattype));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISSetLocalMatType - Specifies the type of local matrix inside the `MATIS`

  Logically Collective.

  Input Parameters:
+ mat   - the matrix
- mtype - the local matrix type

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatSetType()`, `MatType`
@*/
PetscErrorCode MatISSetLocalMatType(Mat mat, MatType mtype)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscUseMethod(mat, "MatISSetLocalMatType_C", (Mat, MatType), (mat, mtype));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISSetLocalMat_IS(Mat mat, Mat local)
{
  Mat_IS   *is = (Mat_IS *)mat->data;
  PetscInt  nrows, ncols, orows, ocols;
  MatType   mtype, otype;
  PetscBool sametype = PETSC_TRUE;

  PetscFunctionBegin;
  if (is->A && !is->islocalref) {
    PetscCall(MatGetSize(is->A, &orows, &ocols));
    PetscCall(MatGetSize(local, &nrows, &ncols));
    PetscCheck(orows == nrows && ocols == ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local MATIS matrix should be of size %" PetscInt_FMT "x%" PetscInt_FMT " (passed a %" PetscInt_FMT "x%" PetscInt_FMT " matrix)", orows, ocols, nrows, ncols);
    PetscCall(MatGetType(local, &mtype));
    PetscCall(MatGetType(is->A, &otype));
    PetscCall(PetscStrcmp(mtype, otype, &sametype));
  }
  PetscCall(PetscObjectReference((PetscObject)local));
  PetscCall(MatDestroy(&is->A));
  is->A = local;
  PetscCall(MatGetType(is->A, &mtype));
  PetscCall(MatISSetLocalMatType(mat, mtype));
  if (!sametype && !is->islocalref) PetscCall(MatISSetUpScatters_Private(mat));
  is->lnnzstate = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISSetLocalMat - Replace the local matrix stored inside a `MATIS` object.

  Not Collective

  Input Parameters:
+ mat   - the matrix
- local - the local matrix

  Level: intermediate

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatISSetLocalMatType`, `MatISGetLocalMat()`
@*/
PetscErrorCode MatISSetLocalMat(Mat mat, Mat local)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
  PetscValidHeaderSpecific(local, MAT_CLASSID, 2);
  PetscUseMethod(mat, "MatISSetLocalMat_C", (Mat, Mat), (mat, local));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatZeroEntries_IS(Mat A)
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(MatZeroEntries(a->A));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatScale_IS(Mat A, PetscScalar a)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(MatScale(is->A, a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetDiagonal_IS(Mat A, Vec v)
{
  Mat_IS *is = (Mat_IS *)A->data;

  PetscFunctionBegin;
  /* get diagonal of the local matrix */
  PetscCall(MatGetDiagonal(is->A, is->y));

  /* scatter diagonal back into global vector */
  PetscCall(VecSet(v, 0));
  PetscCall(VecScatterBegin(is->rctx, is->y, v, ADD_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(is->rctx, is->y, v, ADD_VALUES, SCATTER_REVERSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetOption_IS(Mat A, MatOption op, PetscBool flg)
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(MatSetOption(a->A, op, flg));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatAXPY_IS(Mat Y, PetscScalar a, Mat X, MatStructure str)
{
  Mat_IS *y = (Mat_IS *)Y->data;
  Mat_IS *x;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) {
    PetscBool ismatis;
    PetscCall(PetscObjectTypeCompare((PetscObject)X, MATIS, &ismatis));
    PetscCheck(ismatis, PetscObjectComm((PetscObject)Y), PETSC_ERR_SUP, "Cannot call MatAXPY(Y,a,X,str) with X not of type MATIS");
  }
  x = (Mat_IS *)X->data;
  PetscCall(MatAXPY(y->A, a, x->A, str));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetLocalSubMatrix_IS(Mat A, IS row, IS col, Mat *submat)
{
  Mat                    lA;
  Mat_IS                *matis = (Mat_IS *)A->data;
  ISLocalToGlobalMapping rl2g, cl2g;
  IS                     is;
  const PetscInt        *rg, *rl;
  PetscInt               nrg, rbs, cbs;
  PetscInt               N, M, nrl, i, *idxs;

  PetscFunctionBegin;
  PetscCall(ISGetBlockSize(row, &rbs));
  PetscCall(ISGetBlockSize(col, &cbs));
  PetscCall(ISLocalToGlobalMappingGetIndices(A->rmap->mapping, &rg));
  PetscCall(ISGetLocalSize(row, &nrl));
  PetscCall(ISGetIndices(row, &rl));
  PetscCall(ISLocalToGlobalMappingGetSize(A->rmap->mapping, &nrg));
  if (PetscDefined(USE_DEBUG)) {
    for (i = 0; i < nrl; i++) PetscCheck(rl[i] < nrg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local row index %" PetscInt_FMT " -> %" PetscInt_FMT " greater than maximum possible %" PetscInt_FMT, i, rl[i], nrg);
  }
  if (nrg % rbs) nrg = rbs * (nrg / rbs + 1);
  PetscCall(PetscMalloc1(nrg, &idxs));
  /* map from [0,nrl) to row */
  for (i = 0; i < nrl; i++) idxs[i] = rl[i];
  for (i = nrl; i < nrg; i++) idxs[i] = -1;
  PetscCall(ISRestoreIndices(row, &rl));
  PetscCall(ISLocalToGlobalMappingRestoreIndices(A->rmap->mapping, &rg));
  PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), nrg, idxs, PETSC_OWN_POINTER, &is));
  PetscCall(ISLocalToGlobalMappingCreateIS(is, &rl2g));
  PetscCall(ISLocalToGlobalMappingSetBlockSize(rl2g, rbs));
  PetscCall(ISDestroy(&is));
  /* compute new l2g map for columns */
  if (col != row || matis->rmapping != matis->cmapping || matis->A->rmap->mapping != matis->A->cmap->mapping) {
    const PetscInt *cg, *cl;
    PetscInt        ncg;
    PetscInt        ncl;

    PetscCall(ISLocalToGlobalMappingGetIndices(A->cmap->mapping, &cg));
    PetscCall(ISGetLocalSize(col, &ncl));
    PetscCall(ISGetIndices(col, &cl));
    PetscCall(ISLocalToGlobalMappingGetSize(A->cmap->mapping, &ncg));
    if (PetscDefined(USE_DEBUG)) {
      for (i = 0; i < ncl; i++) PetscCheck(cl[i] < ncg, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local column index %" PetscInt_FMT " -> %" PetscInt_FMT " greater than maximum possible %" PetscInt_FMT, i, cl[i], ncg);
    }
    if (ncg % cbs) ncg = cbs * (ncg / cbs + 1);
    PetscCall(PetscMalloc1(ncg, &idxs));
    /* map from [0,ncl) to col */
    for (i = 0; i < ncl; i++) idxs[i] = cl[i];
    for (i = ncl; i < ncg; i++) idxs[i] = -1;
    PetscCall(ISRestoreIndices(col, &cl));
    PetscCall(ISLocalToGlobalMappingRestoreIndices(A->cmap->mapping, &cg));
    PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), ncg, idxs, PETSC_OWN_POINTER, &is));
    PetscCall(ISLocalToGlobalMappingCreateIS(is, &cl2g));
    PetscCall(ISLocalToGlobalMappingSetBlockSize(cl2g, cbs));
    PetscCall(ISDestroy(&is));
  } else {
    PetscCall(PetscObjectReference((PetscObject)rl2g));
    cl2g = rl2g;
  }

  /* create the MATIS submatrix */
  PetscCall(MatGetSize(A, &M, &N));
  PetscCall(MatCreate(PetscObjectComm((PetscObject)A), submat));
  PetscCall(MatSetSizes(*submat, PETSC_DECIDE, PETSC_DECIDE, M, N));
  PetscCall(MatSetType(*submat, MATIS));
  matis             = (Mat_IS *)((*submat)->data);
  matis->islocalref = A;
  PetscCall(MatSetLocalToGlobalMapping(*submat, rl2g, cl2g));
  PetscCall(MatISGetLocalMat(A, &lA));
  PetscCall(MatISSetLocalMat(*submat, lA));
  PetscCall(ISLocalToGlobalMappingDestroy(&rl2g));
  PetscCall(ISLocalToGlobalMappingDestroy(&cl2g));

  /* remove unsupported ops */
  PetscCall(PetscMemzero((*submat)->ops, sizeof(struct _MatOps)));
  (*submat)->ops->destroy               = MatDestroy_IS;
  (*submat)->ops->setvalueslocal        = MatSetValuesLocal_SubMat_IS;
  (*submat)->ops->setvaluesblockedlocal = MatSetValuesBlockedLocal_SubMat_IS;
  (*submat)->ops->zerorowslocal         = MatZeroRowsLocal_SubMat_IS;
  (*submat)->ops->zerorowscolumnslocal  = MatZeroRowsColumnsLocal_SubMat_IS;
  (*submat)->ops->getlocalsubmatrix     = MatGetLocalSubMatrix_IS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetFromOptions_IS(Mat A, PetscOptionItems PetscOptionsObject)
{
  Mat_IS   *a = (Mat_IS *)A->data;
  char      type[256];
  PetscBool flg;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "MATIS options");
  PetscCall(PetscOptionsDeprecated("-matis_keepassembled", "-mat_is_keepassembled", "3.21", NULL));
  PetscCall(PetscOptionsDeprecated("-matis_fixempty", "-mat_is_fixempty", "3.21", NULL));
  PetscCall(PetscOptionsDeprecated("-matis_storel2l", "-mat_is_storel2l", "3.21", NULL));
  PetscCall(PetscOptionsDeprecated("-matis_localmat_type", "-mat_is_localmat_type", "3.21", NULL));
  PetscCall(PetscOptionsBool("-mat_is_keepassembled", "Store an assembled version if needed", NULL, a->keepassembled, &a->keepassembled, NULL));
  PetscCall(PetscOptionsBool("-mat_is_fixempty", "Fix local matrices in case of empty local rows/columns", "MatISFixLocalEmpty", a->locempty, &a->locempty, NULL));
  PetscCall(PetscOptionsBool("-mat_is_storel2l", "Store local-to-local matrices generated from PtAP operations", "MatISStoreL2L", a->storel2l, &a->storel2l, NULL));
  PetscCall(PetscOptionsBool("-mat_is_allow_repeated", "Allow local repeated entries", "MatISSetAllowRepeated", a->allow_repeated, &a->allow_repeated, NULL));
  PetscCall(PetscOptionsFList("-mat_is_localmat_type", "Matrix type", "MatISSetLocalMatType", MatList, a->lmattype, type, 256, &flg));
  if (flg) PetscCall(MatISSetLocalMatType(A, type));
  if (a->A) PetscCall(MatSetFromOptions(a->A));
  PetscOptionsHeadEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatCreateIS - Creates a "process" unassembled matrix.

  Collective.

  Input Parameters:
+ comm - MPI communicator that will share the matrix
. bs   - block size of the matrix
. m    - local size of left vector used in matrix vector products
. n    - local size of right vector used in matrix vector products
. M    - global size of left vector used in matrix vector products
. N    - global size of right vector used in matrix vector products
. rmap - local to global map for rows
- cmap - local to global map for cols

  Output Parameter:
. A - the resulting matrix

  Level: intermediate

  Notes:
  `m` and `n` are NOT related to the size of the map; they represent the size of the local parts of the distributed vectors
  used in `MatMult()` operations. The local sizes of `rmap` and `cmap` define the size of the local matrices.

  If `rmap` (`cmap`) is `NULL`, then the local row (column) spaces matches the global space.

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatSetLocalToGlobalMapping()`
@*/
PetscErrorCode MatCreateIS(MPI_Comm comm, PetscInt bs, PetscInt m, PetscInt n, PetscInt M, PetscInt N, ISLocalToGlobalMapping rmap, ISLocalToGlobalMapping cmap, Mat *A)
{
  PetscFunctionBegin;
  PetscCall(MatCreate(comm, A));
  PetscCall(MatSetSizes(*A, m, n, M, N));
  if (bs > 0) PetscCall(MatSetBlockSize(*A, bs));
  PetscCall(MatSetType(*A, MATIS));
  PetscCall(MatSetLocalToGlobalMapping(*A, rmap, cmap));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatHasOperation_IS(Mat A, MatOperation op, PetscBool *has)
{
  Mat_IS      *a              = (Mat_IS *)A->data;
  MatOperation tobefiltered[] = {MATOP_MULT_ADD, MATOP_MULT_TRANSPOSE_ADD, MATOP_GET_DIAGONAL_BLOCK, MATOP_INCREASE_OVERLAP};

  PetscFunctionBegin;
  *has = PETSC_FALSE;
  if (!((void **)A->ops)[op] || !a->A) PetscFunctionReturn(PETSC_SUCCESS);
  *has = PETSC_TRUE;
  for (PetscInt i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(tobefiltered); i++)
    if (op == tobefiltered[i]) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(MatHasOperation(a->A, op, has));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetValuesCOO_IS(Mat A, const PetscScalar v[], InsertMode imode)
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCall(MatSetValuesCOO(a->A, v, imode));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetPreallocationCOOLocal_IS(Mat A, PetscCount ncoo, PetscInt coo_i[], PetscInt coo_j[])
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  PetscCheck(a->A, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to provide l2g map first via MatSetLocalToGlobalMapping");
  if (a->A->rmap->mapping || a->A->cmap->mapping) {
    PetscCall(MatSetPreallocationCOOLocal(a->A, ncoo, coo_i, coo_j));
  } else {
    PetscCall(MatSetPreallocationCOO(a->A, ncoo, coo_i, coo_j));
  }
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_IS));
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetPreallocationCOO_IS(Mat A, PetscCount ncoo, PetscInt coo_i[], PetscInt coo_j[])
{
  Mat_IS  *a = (Mat_IS *)A->data;
  PetscInt ncoo_i;

  PetscFunctionBegin;
  PetscCheck(a->A, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to provide l2g map first via MatSetLocalToGlobalMapping");
  PetscCall(PetscIntCast(ncoo, &ncoo_i));
  PetscCall(ISGlobalToLocalMappingApply(a->rmapping, IS_GTOLM_MASK, ncoo_i, coo_i, NULL, coo_i));
  PetscCall(ISGlobalToLocalMappingApply(a->cmapping, IS_GTOLM_MASK, ncoo_i, coo_j, NULL, coo_j));
  PetscCall(MatSetPreallocationCOO(a->A, ncoo, coo_i, coo_j));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetValuesCOO_C", MatSetValuesCOO_IS));
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISGetAssembled_Private(Mat A, Mat *tA)
{
  Mat_IS          *a = (Mat_IS *)A->data;
  PetscObjectState Astate, aAstate       = PETSC_INT_MIN;
  PetscObjectState Annzstate, aAnnzstate = PETSC_INT_MIN;

  PetscFunctionBegin;
  PetscCall(PetscObjectStateGet((PetscObject)A, &Astate));
  Annzstate = A->nonzerostate;
  if (a->assembledA) {
    PetscCall(PetscObjectStateGet((PetscObject)a->assembledA, &aAstate));
    aAnnzstate = a->assembledA->nonzerostate;
  }
  if (aAnnzstate != Annzstate) PetscCall(MatDestroy(&a->assembledA));
  if (Astate != aAstate || !a->assembledA) {
    MatType     aAtype;
    PetscMPIInt size;
    PetscInt    rbs, cbs, bs;

    /* the assembled form is used as temporary storage for parallel operations
       like createsubmatrices and the like, do not waste device memory */
    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(a->cmapping, &cbs));
    PetscCall(ISLocalToGlobalMappingGetBlockSize(a->rmapping, &rbs));
    bs = rbs == cbs ? rbs : 1;
    if (a->assembledA) PetscCall(MatGetType(a->assembledA, &aAtype));
    else if (size > 1) aAtype = bs > 1 ? MATMPIBAIJ : MATMPIAIJ;
    else aAtype = bs > 1 ? MATSEQBAIJ : MATSEQAIJ;

    PetscCall(MatConvert(A, aAtype, a->assembledA ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX, &a->assembledA));
    PetscCall(PetscObjectStateSet((PetscObject)a->assembledA, Astate));
    a->assembledA->nonzerostate = Annzstate;
  }
  PetscCall(PetscObjectReference((PetscObject)a->assembledA));
  *tA = a->assembledA;
  if (!a->keepassembled) PetscCall(MatDestroy(&a->assembledA));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISRestoreAssembled_Private(Mat A, Mat *tA)
{
  PetscFunctionBegin;
  PetscCall(MatDestroy(tA));
  *tA = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatGetDiagonalBlock_IS(Mat A, Mat *dA)
{
  Mat_IS          *a = (Mat_IS *)A->data;
  PetscObjectState Astate, dAstate = PETSC_INT_MIN;

  PetscFunctionBegin;
  PetscCall(PetscObjectStateGet((PetscObject)A, &Astate));
  if (a->dA) PetscCall(PetscObjectStateGet((PetscObject)a->dA, &dAstate));
  if (Astate != dAstate) {
    Mat     tA;
    MatType ltype;

    PetscCall(MatDestroy(&a->dA));
    PetscCall(MatISGetAssembled_Private(A, &tA));
    PetscCall(MatGetDiagonalBlock(tA, &a->dA));
    PetscCall(MatPropagateSymmetryOptions(tA, a->dA));
    PetscCall(MatGetType(a->A, &ltype));
    PetscCall(MatConvert(a->dA, ltype, MAT_INPLACE_MATRIX, &a->dA));
    PetscCall(PetscObjectReference((PetscObject)a->dA));
    PetscCall(MatISRestoreAssembled_Private(A, &tA));
    PetscCall(PetscObjectStateSet((PetscObject)a->dA, Astate));
  }
  *dA = a->dA;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatCreateSubMatrices_IS(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse reuse, Mat *submat[])
{
  Mat tA;

  PetscFunctionBegin;
  PetscCall(MatISGetAssembled_Private(A, &tA));
  PetscCall(MatCreateSubMatrices(tA, n, irow, icol, reuse, submat));
  /* MatCreateSubMatrices_MPIAIJ is a mess at the moment */
#if 0
  {
    Mat_IS    *a = (Mat_IS*)A->data;
    MatType   ltype;
    VecType   vtype;
    char      *flg;

    PetscCall(MatGetType(a->A,&ltype));
    PetscCall(MatGetVecType(a->A,&vtype));
    PetscCall(PetscStrstr(vtype,"cuda",&flg));
    if (!flg) PetscCall(PetscStrstr(vtype,"hip",&flg));
    if (!flg) PetscCall(PetscStrstr(vtype,"kokkos",&flg));
    if (flg) {
      for (PetscInt i = 0; i < n; i++) {
        Mat sA = (*submat)[i];

        PetscCall(MatConvert(sA,ltype,MAT_INPLACE_MATRIX,&sA));
        (*submat)[i] = sA;
      }
    }
  }
#endif
  PetscCall(MatISRestoreAssembled_Private(A, &tA));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatIncreaseOverlap_IS(Mat A, PetscInt n, IS is[], PetscInt ov)
{
  Mat tA;

  PetscFunctionBegin;
  PetscCall(MatISGetAssembled_Private(A, &tA));
  PetscCall(MatIncreaseOverlap(tA, n, is, ov));
  PetscCall(MatISRestoreAssembled_Private(A, &tA));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  MatISGetLocalToGlobalMapping - Gets the local-to-global numbering of the `MATIS` object

  Not Collective

  Input Parameter:
. A - the matrix

  Output Parameters:
+ rmapping - row mapping
- cmapping - column mapping

  Level: advanced

  Note:
  The returned map can be different from the one used to construct the `MATIS` object, since it will not contain negative or repeated indices.

.seealso: [](ch_matrices), `Mat`, `MATIS`, `MatSetLocalToGlobalMapping()`
@*/
PetscErrorCode MatISGetLocalToGlobalMapping(Mat A, ISLocalToGlobalMapping *rmapping, ISLocalToGlobalMapping *cmapping)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidType(A, 1);
  if (rmapping) PetscAssertPointer(rmapping, 2);
  if (cmapping) PetscAssertPointer(cmapping, 3);
  PetscUseMethod(A, "MatISGetLocalToGlobalMapping_C", (Mat, ISLocalToGlobalMapping *, ISLocalToGlobalMapping *), (A, rmapping, cmapping));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatISGetLocalToGlobalMapping_IS(Mat A, ISLocalToGlobalMapping *r, ISLocalToGlobalMapping *c)
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  if (r) *r = a->rmapping;
  if (c) *c = a->cmapping;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatSetBlockSizes_IS(Mat A, PetscInt rbs, PetscInt cbs)
{
  Mat_IS *a = (Mat_IS *)A->data;

  PetscFunctionBegin;
  if (a->A) PetscCall(MatSetBlockSizes(a->A, rbs, cbs));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
  MATIS - MATIS = "is" - A matrix type to be used for non-overlapping domain decomposition methods (e.g. `PCBDDC` or `KSPFETIDP`).
  This stores the matrices in globally unassembled form and the parallel matrix vector product is handled "implicitly".

  Options Database Keys:
+ -mat_type is           - Set the matrix type to `MATIS`.
. -mat_is_allow_repeated - Allow repeated entries in the local part of the local to global maps.
. -mat_is_fixempty       - Fix local matrices in case of empty local rows/columns.
- -mat_is_storel2l       - Store the local-to-local operators generated by the Galerkin process of `MatPtAP()`.

  Level: intermediate

  Notes:
  Options prefix for the inner matrix are given by `-is_mat_xxx`

  You must call `MatSetLocalToGlobalMapping()` before using this matrix type.

  You can do matrix preallocation on the local matrix after you obtain it with
  `MatISGetLocalMat()`; otherwise, you could use `MatISSetPreallocation()` or `MatXAIJSetPreallocation()`

.seealso: [](ch_matrices), `Mat`, `MATIS`, `Mat`, `MatISGetLocalMat()`, `MatSetLocalToGlobalMapping()`, `MatISSetPreallocation()`, `MatCreateIS()`, `PCBDDC`, `KSPFETIDP`
M*/
PETSC_EXTERN PetscErrorCode MatCreate_IS(Mat A)
{
  Mat_IS *a;

  PetscFunctionBegin;
  PetscCall(PetscNew(&a));
  PetscCall(PetscStrallocpy(MATAIJ, &a->lmattype));
  A->data = (void *)a;

  /* matrix ops */
  PetscCall(PetscMemzero(A->ops, sizeof(struct _MatOps)));
  A->ops->mult                    = MatMult_IS;
  A->ops->multadd                 = MatMultAdd_IS;
  A->ops->multtranspose           = MatMultTranspose_IS;
  A->ops->multtransposeadd        = MatMultTransposeAdd_IS;
  A->ops->destroy                 = MatDestroy_IS;
  A->ops->setlocaltoglobalmapping = MatSetLocalToGlobalMapping_IS;
  A->ops->setvalues               = MatSetValues_IS;
  A->ops->setvaluesblocked        = MatSetValuesBlocked_IS;
  A->ops->setvalueslocal          = MatSetValuesLocal_IS;
  A->ops->setvaluesblockedlocal   = MatSetValuesBlockedLocal_IS;
  A->ops->zerorows                = MatZeroRows_IS;
  A->ops->zerorowscolumns         = MatZeroRowsColumns_IS;
  A->ops->assemblybegin           = MatAssemblyBegin_IS;
  A->ops->assemblyend             = MatAssemblyEnd_IS;
  A->ops->view                    = MatView_IS;
  A->ops->load                    = MatLoad_IS;
  A->ops->zeroentries             = MatZeroEntries_IS;
  A->ops->scale                   = MatScale_IS;
  A->ops->getdiagonal             = MatGetDiagonal_IS;
  A->ops->setoption               = MatSetOption_IS;
  A->ops->ishermitian             = MatIsHermitian_IS;
  A->ops->issymmetric             = MatIsSymmetric_IS;
  A->ops->isstructurallysymmetric = MatIsStructurallySymmetric_IS;
  A->ops->duplicate               = MatDuplicate_IS;
  A->ops->missingdiagonal         = MatMissingDiagonal_IS;
  A->ops->copy                    = MatCopy_IS;
  A->ops->getlocalsubmatrix       = MatGetLocalSubMatrix_IS;
  A->ops->createsubmatrix         = MatCreateSubMatrix_IS;
  A->ops->axpy                    = MatAXPY_IS;
  A->ops->diagonalset             = MatDiagonalSet_IS;
  A->ops->shift                   = MatShift_IS;
  A->ops->transpose               = MatTranspose_IS;
  A->ops->getinfo                 = MatGetInfo_IS;
  A->ops->diagonalscale           = MatDiagonalScale_IS;
  A->ops->setfromoptions          = MatSetFromOptions_IS;
  A->ops->setup                   = MatSetUp_IS;
  A->ops->hasoperation            = MatHasOperation_IS;
  A->ops->getdiagonalblock        = MatGetDiagonalBlock_IS;
  A->ops->createsubmatrices       = MatCreateSubMatrices_IS;
  A->ops->increaseoverlap         = MatIncreaseOverlap_IS;
  A->ops->setblocksizes           = MatSetBlockSizes_IS;

  /* special MATIS functions */
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetLocalMatType_C", MatISSetLocalMatType_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISGetLocalMat_C", MatISGetLocalMat_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISRestoreLocalMat_C", MatISRestoreLocalMat_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetLocalMat_C", MatISSetLocalMat_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetPreallocation_C", MatISSetPreallocation_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISSetAllowRepeated_C", MatISSetAllowRepeated_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISStoreL2L_C", MatISStoreL2L_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISFixLocalEmpty_C", MatISFixLocalEmpty_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatISGetLocalToGlobalMapping_C", MatISGetLocalToGlobalMapping_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpiaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpibaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_mpisbaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqbaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_seqsbaij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_is_aij_C", MatConvert_IS_XAIJ));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOOLocal_C", MatSetPreallocationCOOLocal_IS));
  PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_IS));
  PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATIS));
  PetscFunctionReturn(PETSC_SUCCESS);
}